# 9.6 Solve geometry applications: volume and surface area  (Page 7/11)

 Page 7 / 11

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.

678.24 cu. in.

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.

128.2 cu. in.

## Summary of geometry formulas

The following charts summarize all of the formulas covered in this chapter.  ## Key concepts

• Volume and Surface Area of a Rectangular Solid
• $V=LWH$
• $S=2LH+2LW+2WH$
• Volume and Surface Area of a Cube
• $V={s}^{3}$
• $S=6{s}^{2}$
• Volume and Surface Area of a Sphere
• $V=\frac{4}{3}\pi {r}^{3}$
• $S=4\pi {r}^{2}$
• Volume and Surface Area of a Cylinder
• $V=\pi {r}^{2}h$
• $S=2\pi {r}^{2}+2\pi rh$
• Volume of a Cone
• For a cone with radius $r$ and height $h$ :
Volume: $V=\frac{1}{3}\pi {r}^{2}h$

## Practice makes perfect

Find Volume and Surface Area of Rectangular Solids

In the following exercises, 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

1. 9 cu. m
2. 27 sq. m

length $5$ feet, width $8$ feet, height $2.5$ feet

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

1. 17.64 cu. yd.
2. 41.58 sq. yd.

length $8.8$ centimeters, width $6.5$ centimeters, height $4.2$ centimeters

In the following exercises, solve.

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

1. 1,024 cu. ft
2. 640 sq. ft

Gift box A rectangular gift box has length $26$ inches, width $16$ inches, and height $4$ inches. Find its volume and surface area.

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

1. 3,350.49 cu. cm
2. 1,622.42 sq. cm

Shipping container A rectangular shipping container has length $22.8$ feet, width $8.5$ feet, and height $8.2$ feet. Find its volume and surface area.

In the following exercises, find the volume and the surface area of the cube with the given side length.

$5$ centimeters

1. 125 cu. cm
2. 150 sq. cm

$6$ inches

$10.4$ feet

1. 1124.864 cu. ft.
2. 648.96 sq. ft

$12.5$ meters

In the following exercises, 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.

1. 262,144 cu. ft
2. 24,576 sq. ft

Museum A cube-shaped museum has sides $45$ meters long. Find its volume and surface area.

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

1. 21.952 cu. m
2. 47.04 sq. m

Tissue box A box of tissues is a cube with sides 4.5 inches long. Find its volume and surface area.

Find the Volume and Surface Area of Spheres In the following exercises, find the volume and the surface area of the sphere with the given radius. Round answers to the nearest hundredth.

$3$ centimeters

1. 113.04 cu. cm
2. 113.04 sq. cm

$9$ inches

$7.5$ feet

1. 1,766.25 cu. ft
2. 706.5 sq. ft

$2.1$ yards

In the following exercises, solve. Round answers to the nearest hundredth.

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

1. 14,130 cu. in.
2. 2,826 sq. in.

Balloon ride The Great Park Balloon is a big orange sphere with a radius of $36$ feet . Find its volume and surface area.

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