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In the following exercises, solve using the properties of circles. Round answers to the nearest hundredth.

A circular mosaic has radius 3 meters. Find the

  1. circumference
  2. area of the mosaic

  1. 18.84 m
  2. 28.26 sq. m

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A circular fountain has radius 8 feet. Find the

  • circumference
  • area of the fountain

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Find the diameter of a circle with circumference 150.72 inches.

48 in.

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Find the radius of a circle with circumference 345.4 centimeters

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Find the Area of Irregular Figures

In the following exercises, find the area of each shaded region.

Solve Geometry Applications: Volume and Surface Area

Find Volume and Surface Area of Rectangular Solids

In the following exercises, find the

  1. volume
  2. surface area of the rectangular solid

a rectangular solid with length 14 centimeters, width 4.5 centimeters, and height 10 centimeters

  1. 630 cu. cm
  2. 496 sq. cm

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a cube with sides that are 3 feet long

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a cube of tofu with sides 2.5 inches

  1. 15.625 cu. in.
  2. 37.5 sq. in.

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a rectangular carton with length 32 inches, width 18 inches, and height 10 inches

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Find Volume and Surface Area of Spheres

In the following exercises, find the

  1. volume
  2. surface area of the sphere.

a sphere with radius 4 yards

  • 267.95 cu. yd.
  • 200.96 sq. yd.

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a sphere with radius 12 meters

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a baseball with radius 1.45 inches

  1. 12.76 cu. in.
  2. 26.41 sq. in.

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a soccer ball with radius 22 centimeters

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Find Volume and Surface Area of Cylinders

In the following exercises, find the

  1. volume
  2. surface area of the cylinder

a cylinder with radius 2 yards and height 6 yards

  1. 75.36 cu. yd.
  2. 100.48 sq. yd.

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a cylinder with diameter 18 inches and height 40 inches

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a juice can with diameter 8 centimeters and height 15 centimeters

  1. 753.6 cu. cm
  2. 477.28 sq. cm

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a cylindrical pylon with diameter 0.8 feet and height 2.5 feet

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Find Volume of Cones

In the following exercises, find the volume of the cone.

a cone with height 5 meters and radius 1 meter

5.233 cu. m

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a cone with height 24 feet and radius 8 feet

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a cone-shaped water cup with diameter 2.6 inches and height 2.6 inches

4.599 cu. in.

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a cone-shaped pile of gravel with diameter 6 yards and height 5 yards

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Solve a Formula for a Specific Variable

Use the Distance, Rate, and Time Formula

In the following exercises, solve using the formula for distance, rate, and time.

A plane flew 4 hours at 380 miles per hour. What distance was covered?

1520 miles

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Gus rode his bike for 1 1 2 hours at 8 miles per hour. How far did he ride?

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Jack is driving from Bangor to Portland at a rate of 68 miles per hour. The distance is 107 miles. To the nearest tenth of an hour, how long will the trip take?

1.6 hours

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Jasmine took the bus from Pittsburgh to Philadelphia. The distance is 305 miles and the trip took 5 hours. What was the speed of the bus?

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Solve a Formula for a Specific Variable

In the following exercises, use the formula d = r t .

Solve for t :

  1. when d = 403 and r = 65
  2. in general
  1. t = 6.2
  2. t = d r
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Solve for r :

  1. when d = 750 and t = 15
  2. in general
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In the following exercises, use the formula A = 1 2 b h .

Solve for b :

  1. when A = 416 and h = 32
  2. in general
  1. b = 26
  2. b = 2 A h
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Solve for h :

  1. when A = 48 and b = 8
  2. in general
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In the following exercises, use the formula I = P r t .

Solve for the principal, P , for:

  1. I = $720 , r = 4% , t = 3 years
  2. in general
  1. P = $6000
  2. P = I ( r t )
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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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