Volumes and Surface Area

\(\begin{aligned}
\text{A cube has an edge length of 41 inches. What is the volume, in cubic inches, of the cube?}
\end{aligned}\)

\(\begin{aligned}
&\text{The length of each edge of a box is 29 inches. Each side of the box is in the shape of a square. }\\
&\text{The box does not have a lid. What is the exterior surface area, in square inches, of this box}\\&\text{without a lid?}\end{aligned}\)

\(\begin{aligned}&\text{The length of each edge of a box is 94 centimeters. Each side of the box is in the shape of a}\\&\text{square. The box does not have a lid. What is the exterior surface area, in square }\underline{\text{meters}},\text{ of}\\&\text{this box without a lid? (1 meter = 100 centimeters)}\end{aligned}\)

\(\begin{aligned}
&\text{The surface area of a cube is 6}\left(\frac{a}{4}\right)^{2},\text{where }a\text{ is a positive constant.}\\
&\text{Which of the following gives the perimeter of one face of the cube?}\\\end{aligned}\)

\(\begin{aligned}
&\text{To study fluctuations in the leaf water potential, samples of wood were taken from 26 trees and}\\
&\text{cut in the shape of a cube. The length of the edge of one of these cubes is 2.00 centimeters. If}\\
&\text{this cube has a mass of 5.12 grams, what is the density of this cube in grams per cubic }\\
&\mathrm{centimeter?}\end{aligned}\)

\(\begin{aligned}
&\text{A cube has a volume of }79,507\text{ cubic units. What is the surface area, in square units, of}\\
&\text{the cube?}\end{aligned}\)

\(\begin{aligned}&\text{The edge length, in inches, of cube Y is }\frac{3}{64}\text{ the edge length, in inches, of cube X. The surface}\\&\text{area, in square inches, of cube Y is }n\text{ times the surface area, in square inches, of cube X.}\\&\text{What is the value of }n?\\\end{aligned}\)

\(\begin{aligned}
&\text{What is the volume, in cubic centimeters, of a right rectangular prism that has a length of 4}\\
&\text{centimeters, a width of 9 centimeters, and a height of 10 centimeters?}\end{aligned}\)

\(\begin{aligned}
&\text{A right rectangular prism has a length of 26 centimeters (cm), a width of 16 cm, and a }\\
&\text{height of 14 cm. What is the surface area, in cm} ^{2},\text{ of the right rectangular prism?}\end{aligned}\)

\(\begin{aligned}
&\text{A granite block in the shape of a right rectangular prism has dimensions 30 centimeters by} \\
&\text{40 centimeters by 50 centimeters. The block has a density of 2.8 grams per cubic centimeter.}\\
&\text{What is the mass of the block, in grams? (Density is mass per unit volume.)}\end{aligned}\)

\(\begin{aligned}
&\text{A raised garden is in the shape of a right rectangular prism. Its base has a}\\
&\text{width of 3 feet and a length of 27 feet, and it will be filled 24  }\underline{\text{inches}}\text{  high with}\\
&\text{topsoil. The total cost of the topsoil needed to fill the garden to this height is}\\
&\text{234 dollars. What is the unit cost, in dollars per }\underline{\text{cubic yard}}\text{, for the topsoil?}\\&(1\text{ yard}=3\text{ feet};1\text{ foot}=12\text{ inches})\end{aligned}\)

\(\begin{aligned}&\text{The volume of a right rectangular prism with a square base is 539 cubic centimeters. If the}\\&\text{area of each of the four lateral faces is 77 square centimeters, what is the height, in}\\&\text{centimeters, of the prism?}\end{aligned}\)

\(\begin{aligned}
&\text{The volume of a right rectangular prism with a square base is 1,792 cubic centimeters. If}\\
&\text{the area of the square base is 64 square centimeters, what is the area, in square centimeters, }\\
&\text{of one of the four lateral faces of the prism?}\\
\end{aligned}\)

\(\begin{aligned}&\text{A right rectangular prism has a base area of 56}t\text{ square centimeters (cm}^2).\text{ The length of}\\&\text{the base of the rectangular prism is }\frac{14}{3}\text{ cm, and the height of the rectangular prism is 3 cm }.\\&\text{Which expression represents the surface area, in cm}^2,\text{of the rectangular prism ?}\end{aligned}\)

\(\begin{aligned}
&\text{A right rectangular prism has a base area of }28p\text{ square centimeters }\left(\mathrm{cm}^2\right).\text{The length of}\\
&\text{the base of the rectangular prism is 12 cm, and the height of the rectangular prism is 4 cm.}\\
&\text{Which expression represents the surface area, in cm}^2,\text{of the right rectangular prism?}\end{aligned}\)

\(\begin{aligned}
&\text{Two identical rectangular prisms each have a height of 90 centimeters (cm).}\\
&\text{The base of each prism is a square, and the surface area of each prism is }K \text{ cm}^ 2.\\
&\text{If the prisms are glued together along a square base,}\text{ the resulting prism has a }\\
&\text{surface area of }\frac{92}{47}K\text{ cm}^{2}.\text{ What is the side length, in cm, of each square base?}\end{aligned}\)

\(\begin{aligned}
&\text{Right rectangular prism X is similar to right rectangular prism Y. The surface area of right}\\
&\text{rectangular prism X is 58 square centimeters (cm}^{2}),\text{ and the surface area of right}\\
&\text{rectangular prism Y is 1,450 cm}^{2}.\text{ The volume of right rectangular prism Y is}\\
&\text{1,250 cubic centimeters (cm}^3).\text { What is the sum of the volumes, in cm}^3,\text{ of right }\\
&\text{rectangular prism X and right rectangular prism Y?}\end{aligned}\)

\(\begin{aligned}
&\text{A triangular prism has a height of 9 centimeters (cm) and a volume of 234 cm}^3.\text{ What is}\\
&\text{the area, in cm}^2,\text{of the base of the prism? (The volume of a triangular prism is equal to }Bh,\\&\text{where }B\text{ is the area of the base and }h\text{ is the height of the prism.})\end{aligned}\)

\(\begin{aligned}
&\text{The points }(0, 15),~(10, 8), \text{ and }(10,3)\text{ are shown in the }xy\text{-plane, where the }x \text{ and } y\text{-axis }\\
&\text{are measured in units.}\end{aligned}\)

\(\begin{aligned}&\text{Three points define one of the bases of a triangular prism. The distance between the two}\\&\text{bases of the prism is 20 units. What is the volume, in cubic units, of the prism?}\end{aligned}\)

\(\begin{aligned}
&\text{A right circular cylinder has a height of 6 inches. The radius of the base of the cylinder}\\
&\text{is 5 inches. What is the volume, in cubic inches, of the cylinder?}\end{aligned}\)

\(\begin{aligned}
&\text{A cylinder has a diameter of 14 inches and a height of 8 inches. What is the volume, in cubic}\\&\text{inches, of the cylinder?}\end{aligned}\)

\(\begin{aligned}
&\text{A right circular cylinder has a radius of 12 centimeters and a volume of }2,448\pi \text{ cubic centimeters.}\\
&\text{What is the height, in centimeters, of the cylinder?}\end{aligned}\)

\(\begin{aligned}
&\text{A dairy farmer uses a storage silo that is in the shape of the right circular cylinder above.}\\
&\text{If the volume of the silo is }72\pi\text{ cubic yards, what is the }\underline{\text{diameter}}\text{ of the base of the cylinder,}\\&\text{in yards?}\end{aligned}\)

\(\begin{aligned}
&\text{The circumference of the base of a right circular cylinder is }6\pi\text{ meters, and the height}\\
&\text{of the cylinder is 19 meters. What is the volume, in cubic meters, of the cylinder?}\end{aligned}\)

\(\begin{aligned}
&\text{The height of a right circular cylinder is 6 inches longer than its radius, and the surface area}\\
&\text{of the cylinder is 1,080}\pi\text{ square inches. What is the cylinder’s radius, in inches?}\end{aligned}\)

\(\begin{aligned}
&\text{The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic}\\
&\text{centimeters, of a right circular cylinder with twice the radius and half the height of cylinder A?}\\
\end{aligned}\)

\(\begin{aligned}
&\text{The figure shown is a right circular cylinder with a radius of }r\text{ and a height of }h.\text{ A second}\\
&\text{right circular cylinder (not shown) has a volume that is 576 times as large as the volume of}\\
&\text{the cylinder shown. Which of the following could represent the radius }R,\text{ in terms of }r,\text{ and}\\
&\text{the height }H,\text{ in terms of }h,\text{ of the second cylinder?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~\begin{array}{|c|c|}\hline\\&~\text{ Volume (cubic units) }~\\\\\hline~~\\\text{Right circular cylinder A}~~&112\pi\\\\\hline~~\\\text{ Right circular cylinder B }~~&3,024\pi\\\\\hline\end{array}\\\\
&\text{The table shows the volume of two similar solids, right circular cylinder A }\\
&\text{and right circular cylinder B. The radius of right circular cylinder A is 4 units.}\\
&\text{The surface area of right circular cylinder A is }k\pi\text{ square units, and the}\\
&\text{surface area of right circular cylinder B is }n\pi\text{ square units, where }k\text{ and }n\\
&\text{are constants. What is the value of }n-k?\text{ (The surface area of a right }\\&\text{radius }r\text{ and height }h\mathrm{~is~}2\pi r^{2}+2\pi rh.)\end{aligned}\)

\(\begin{aligned}&\text{In the figure, a hollow steel pipe is in the shape of a right circular cylinder. The steel pipe has an outside}\\&\text{diameter of 48 inches, a wall thickness of }\frac{3}{8}\text{ inches, and a height of 138 inches. Which of the following is}\\&\text{closest to the volume, in cubic inches, of the wall of this steel pipe?}\end{aligned}\)

\(\begin{aligned}
&\text{A right circular cone has a height of 13 centimeters (cm) and a base with a radius of 6 cm.}\\
&\text{What is the volume, in cm}^{3}\text{, }\text{of this cone?}\end{aligned}\)

\(\begin{aligned}
&\text{A right circular cone has a base diameter of 28 inches and a height of 6 inches. The}\\
&\text{volume of this cone is }k\pi\text{ cubic inches. What is the value of }k?\end{aligned}\)

\(\begin{aligned}
&\text{A right circular cone has a volume of }24\pi\text{ cubic inches. If the height of the cone is 2 inches,}\\
&\text{what is the radius, in inches, of the base of the cone?}\end{aligned}\)

\(\begin{aligned}
&\text{A right circular cone has a volume of }2,700\pi\text{ cubic centimeters and the area of its base }\\
&\text{is }225\pi\text{ square centimeters. What is the slant height, in centimeters, of this cone?}\end{aligned}\)

\(\begin{aligned}
&\text{For the right circular cone shown, }B\text{ is a point on the circumference of the base, and the}\\
&\text{length of segment }AB\text{ (not shown) is 84 centimeters. If the height of the cone is 42}\\
&\text{centimeters and the volume of the cone is }k\pi\text{ cubic centimeters, what is the value of }k?
\end{aligned}\)

\(\text{A sphere has a radius of }\frac{8}{3}\text{ feet. What is the volume, in cubic feet, of the sphere?}
\)

\(\begin{aligned}
&\text{The density of a certain type of marble stone is 2.6000 grams per cubic centimeter. If a }\\
&\text{sample of this type of stone is in the shape of a sphere with a diameter of 31.000 }\\
&\text{centimeters, what is the mass of this sample, in grams, to the nearest whole number? (Use}\\&\text{3.14159 for }\pi.)\end{aligned}\)

\(\begin{aligned}&\text{A hemisphere is half of a sphere. If a hemisphere has a radius of 69 inches, which of the}\\
&\text{following is closest to the volume, in cubic inches, of this hemisphere?}\end{aligned}\)

\(\begin{aligned}
&\text{A cube has an edge length of 68 inches. A solid sphere with a radius of 34 inches is inside the cube}\\
&\text{such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is }\\
&\text{the volume of the space in the cube }\underline{\text{not}}\text{ taken up by the sphere?}\end{aligned}\)

\(\begin{aligned}&\text{The right square pyramid shown has a height of 9 centimeters (cm). The length, in cm, of}\\&\text{one edge of the pyramid’s base is }\frac{13}{3}\text{ times the height of the pyramid. What is the volume,}\\&\text{in cm}^3\text{, of the pyramid}?\end{aligned}\)

\(\begin{aligned}
&\text{A right square pyramid has a height of 12 inches and a volume of 1,296 cubic inches.}\\
&\text{What is the perimeter, in inches, of the base of this pyramid?}\end{aligned}\)

\(\begin{aligned}
&\text{A right square pyramid has a height of 11 centimeters (cm). A second right square pyramid}\\
&\text{has a height of 22 centimeters. The area of the base of each of the two pyramids is 100 cm}^{2}.\\
&\text{Which of the following is closest to the difference in the surface area of the second pyramid}\\
&\text{and the surface area of the first pyramid, in cm}^{2}~?\end{aligned}\)

\(\begin{aligned}
&\text{A right square pyramid has a surface area of }100+20\sqrt{146}\text{ square inches, which includes}\\
&\text{a base area of 100 square inches. What is the height, in inches, of this pyramid?}\end{aligned}\)

\(\begin{aligned}
&\text{A right square pyramid has a total surface area of 70,560 square inches, and the combined}\\
&\text{surface area of the four lateral faces of this pyramid is 38,160 square inches. What is the}\\
&\text{height, in inches, of this pyramid?}\end{aligned}\)

\(\begin{aligned}&\text{A right square pyramid has a surface area of 75,264 square inches, which includes a base}\\&\text{area of 36,864 square inches. What is the slant height, in inches, of this pyramid?}\end{aligned}\)

\(\begin{aligned}
&\text{The figure shown is a right rectangular pyramid, where }\ell=18\text{ units},w=9\text{ units},\\
&\text{and }h=12\text{ units. What is the surface area, in square units, of the pyramid?}\end{aligned}\)

\(\begin{aligned}
&\text{A right triangular pyramid has exactly six edges. Each of these edges is 96}\\
&\text{centimeters long. If the surface area of the pyramid is }k\sqrt{3}\text{ square}\\
&\text{centimeters, what is the value of }k?\end{aligned}\)