9.6 Solve Geometry Applications: Volume and Surface Area

Before you get started, take this readiness quiz.

Evaluate $x^{3}$ when $x = 5 .$
If you missed this problem, review the reference.

Evaluate $2^{x}$ when $x = 5 .$
If you missed this problem, review the reference.

Find the area of a circle with radius $\frac{7}{2} .$
If you missed this problem, review the reference.

Find the ⓐ volume and ⓑ surface area of rectangular solid with the: length $8$ feet, width $9$ feet, and height $11$ feet.

Find the ⓐ volume and ⓑ surface area of rectangular solid with the: length $15$ feet, width $12$ feet, and height $8$ feet.

A rectangular box has length $9$ feet, width $4$ feet, and height $6$ feet. Find its ⓐ volume and ⓑ surface area.

A rectangular suitcase has length $22$ inches, width $14$ inches, and height $9$ inches. Find its ⓐ volume and ⓑ surface area.

For a cube with side 4.5 meters, find the ⓐ volume and ⓑ surface area of the cube.

For a cube with side 7.3 yards, find the ⓐ volume and ⓑ surface area of the cube.

A packing box is a cube measuring $4$ feet on each side. Find its ⓐ volume and ⓑ surface area.

A wall is made up of cube-shaped bricks. Each cube is $16$ inches on each side. Find the ⓐ volume and ⓑ surface area of each cube.

Find the ⓐ volume and ⓑ surface area of a sphere with radius 3 centimeters.

Find the ⓐ volume and ⓑ surface area of each sphere with a radius of $1$ foot

A beach ball is in the shape of a sphere with radius of $9$ inches. Find its ⓐ volume and ⓑ surface area.

A Roman statue depicts Atlas holding a globe with radius of $1.5$ feet. Find the ⓐ volume and ⓑ surface area of the globe.

Find the ⓐ volume and ⓑ surface area of the cylinder with radius 4 cm and height 7cm.

Find the ⓐ volume and ⓑ surface area of the cylinder with given radius 2 ft and height 8 ft.

Find the ⓐ volume and ⓑ surface area of a can of paint with radius 8 centimeters and height 19 centimeters. Assume the can is shaped exactly like a cylinder.

Find the ⓐ volume and ⓑ surface area of a cylindrical drum with radius 2.7 feet and height 4 feet. Assume the drum is shaped exactly like a cylinder.

Find the volume of a cone with height $7$ inches and radius $3$ inches

Find the volume of a cone with height $9$ centimeters and radius $5$ centimeters

How many cubic inches of candy will fit in a cone-shaped piñata that is $18$ inches long and $12$ inches across its base? Round the answer to the nearest hundredth.

What is the volume of a cone-shaped party hat that is $10$ inches tall and $7$ inches across at the base? Round the answer to the nearest hundredth.

Find ⓐ the volume and ⓑ the surface area of the rectangular solid with the given dimensions.

length $2$ meters, width $1.5$ meters, height $3$ meters

Find ⓐ the volume and ⓑ the surface area of the rectangular solid with the given dimensions.

length $3.5$ yards, width $2.1$ yards, height $2.4$ yards

Solve.

Moving van A rectangular moving van has length $16$ feet, width $8$ feet, and height $8$ feet. Find its ⓐ volume and ⓑ surface area.

Solve.

Carton A rectangular carton has length $21.3$ cm, width $24.2$ cm, and height $6.5$ cm. Find its ⓐ volume and ⓑ surface area.

Find ⓐ the volume and ⓑ the surface area of the cube with the given side length.

$5$ centimeters

Find ⓐ the volume and ⓑ the surface area of the cube with the given side length.

$10.4$ feet

Solve.

Science center Each side of the cube at the Discovery Science Center in Santa Ana is $64$ feet long. Find its ⓐ volume and ⓑ surface area.

Solve.

Base of statue The base of a statue is a cube with sides $2.8$ meters long. Find its ⓐ volume and ⓑ surface area.

Find ⓐ the volume and ⓑ the surface area of the sphere with the given radius. Round answers to the nearest hundredth.

$3$ centimeters

Find ⓐ the volume and ⓑ the surface area of the sphere with the given radius. Round answers to the nearest hundredth.

$7.5$ feet

Solve. Round answers to the nearest hundredth.

Exercise ball An exercise ball has a radius of $15$ inches. Find its ⓐ volume and ⓑ surface area.

Solve. Round answers to the nearest hundredth.

Golf ball A golf ball has a radius of $4.5$ centimeters. Find its ⓐ volume and ⓑ surface area.

Find ⓐ the volume and ⓑ the surface area of the cylinder with the given radius and height. Round answers to the nearest hundredth.

radius $3$ feet, height $9$ feet

Find ⓐ the volume and ⓑ the surface area of the cylinder with the given radius and height. Round answers to the nearest hundredth.

radius $1.5$ meters, height $4.2$ meters

Solve. Round answers to the nearest hundredth.

Coffee can A can of coffee has a radius of $5$ cm and a height of $13$ cm. Find its ⓐ volume and ⓑ surface area.

Solve. Round answers to the nearest hundredth.

Barber shop pole A cylindrical barber shop pole has a diameter of $6$ inches and height of $24$ inches. Find its ⓐ volume and ⓑ surface area.

Find the volume of the cone with the given dimensions. Round answers to the nearest hundredth.

height $9$ feet and radius $2$ feet

Find the volume of the cone with the given dimensions. Round answers to the nearest hundredth.

height $12.4$ centimeters and radius $5$ cm

Solve. Round answers to the nearest hundredth.

Teepee What is the volume of a cone-shaped teepee tent that is $10$ feet tall and $10$ feet across at the base?

Solve. Round answers to the nearest hundredth.

Silo What is the volume of a cone-shaped silo that is $50$ feet tall and $70$ feet across at the base?

The formulas for the volume of a cylinder and a cone are similar. Explain how you can remember which formula goes with which shape.