Resources

Resources

Volume of cubes and rectangular prisms: word problems

The speed of a baseball

x

seconds after the pitcher releases it is given by the function

f(x)

. The speed is measured in meters per second.

\newline

f(0.3) = 39.8

\newline

\newline

(A) The ball traveled

39.8

0.3

seconds of being released.

\newline

(B) The ball has a speed of

39.8

meters per second

0.3

seconds after it's released.

The speed of a baseball

x

seconds after the pitcher releases it is given by the function

f(x)

. The speed is measured in meters per second.

\newline

f(0.3) = 39.8

\newline

\newline

(A)The ball has a speed of

39.8

meters per second

0.3

seconds after it's released.

\newline

(B)The ball traveled

39.8

0.3

seconds of being released.

The width of a rectangle measures

(6 f+g)

centimeters, and its length measures

(2 f+7 g)

centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

\newline

16 f+16

\newline

8+8 f

\newline

16 g+16 f

\newline

1+14 g+16 f

The width of a rectangle measures

(9 p+8 q)

centimeters, and its length measures

(7 p-4 q)

centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

\newline

4+16 p

\newline

8-8 q+32 p

\newline

32 p+8 q

\newline

32 p+8

The width of a rectangle measures

(6.9 p-8.9 q)

centimeters, and its length measures

(7.7 p-3.3 q)

centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

\newline

14.6 p-12.2

\newline

29.2 p-24.4

\newline

29.2 p-6.6 q-8.9

\newline

29.2 p-24.4 q

The width of a rectangle measures

(5.7 n+8.8)

centimeters, and its length measures

(6.1 n+3.6)

centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

\newline

9.7+14.5 n

\newline

19.4+29 n

\newline

12.4+11.8 n

\newline

24.8+23.6 n

The width of a rectangle measures

(2.9 p-3.9)

centimeters, and its length measures

(9.4 p-3.5)

centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

\newline

-14.8+24.6 p

\newline

-7.4+12.3 p

\newline

-p+5.9

\newline

-2 p+11.8

The width of a rectangle measures

(1.3 b-1.6)

centimeters, and its length measures

(9.9 b+8.6)

centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

\newline

-0.6 b+37

\newline

7+11.2 b

\newline

22.4 b+14

\newline

-0.3 b+18.5

A triangle has side lengths of

(9.1 g-3.1)

(1.4 g+4.2)

centimeters, and

(1.9 h+4.4)

centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

\newline

6.3 h+10.5 g+1.1

\newline

5.6+6.3 h+6 g

\newline

10.5 g+1.9 h+5.5

\newline

11.6 g+6.3 h

The plot in the

\text{TB}

-plane shows the brewing time,

B

, defined as the time it takes for a tea packet to reach a caffeine concentration of

100

milligrams per liter with water at a temperature of

T

degrees Celsius.

\newline

Which of the following equations best models the relationship between

\newline

B

T

\newline

1

\newline

B=9\times0.66^{T}

\newline

B=9\times0.96^{T}

\newline

B=25\times0.66^{T}

\newline

B=25\times0.96^{T}

V=\pi r^{2}h

\newline

The formula gives the volume

V

of a right circular cylinder with radius

r

h

. What is the volume, in cubic inches, of a right circular cylinder with a radius of

3

inches and a height of

2

\newline

1

\newline

5\pi

\newline

6\pi

\newline

12\pi

\newline

18\pi

Without dividing, determine if

74

814

is divisible by

9

and explain how you know.

\newline

74,814 \square

9

Without dividing, determine if

87

848

is divisible by

4

and explain how you know.

\newline

87,848 \square

4

Without dividing, determine if

72

827

is divisible by

4

and explain how you know.

\newline

72,827 \square

4

Without dividing, determine if

27

783

is divisible by

5

and explain how you know.

\newline

27

783

\square

5

Find the volume of each geometric figure in the picture below. Then find the volume of the entire figure.

\newline

Volume of the Rectangular Prism:

V=

\newline

60

\newline

v

\newline

Yolume of the Rectangular Pyramid:

V=

\newline

20

\newline

v

\newline

Volume of the Entire Figure:

V=

\newline

80

\newline

v

\newline

\newline

1 / 1

\newline

All volume is measured in cubir unite

What is the volume, in cubic in, of a cylinder with a height of

17

in and a base radius of

8

in, to the nearest tenths place?

\newline

V=

A cylinder has a base diameter of

6

feet and a height of

18

feet. What is its volume in cubic feet, to the nearest tenths place?

\newline

{ }^{3}

\newline

A pyramid has a square base. Each side of the base is

20 \mathrm{in}

. The height of the pyramid is

14 \mathrm{in}

. What is the volume of the pyramid?

A pyramid has a square base. Each side of the base is

20\,\text{in}

. The height of the pyramid is

14\,\text{in}

. What is the volume of the pyramid?

A cylinder and a cone have the same base and altitude. If the volume of the cone is

30

cubic inches, what is the volume of the cylinder?

\newline

10

\newline

15

\newline

30

\newline

60

\newline

90

Barbara wants a small round area rug for her bedroom. If the area of the rug has to be less than

50

square feet, what is the greatest diameter that the rug can be? Use

3

14

\pi

\newline

6

\newline

7

\newline

8

Find the volume of a rectangular prism with a length of

20

\text{in}

15

8

\text{in}

and a height of

18

3

\text{in}

, to the nearest tenth of a cubic inch.

\newline

\text{in}

^{3}

Find the volume of a pyramid with a square base, where the perimeter of the base is

13

2

\text{in}

and the height of the pyramid is

6.6

\mathrm{in}

. Round your answer to the nearest tenth of a cubic inch.

\newline

\text{in}

^{3}

What is the volume of a cylinder with a height of

5

5

\text{in}

and a base with a diameter of

11

4

\text{in}

, to the nearest tenth of a cubic inch?

\newline

\text{in}

^{3}

What is the volume of a cylinder with a height of

3

3

\text{in}

and a base with a radius of

4

3

\text{in}

, to the nearest tenth of a cubic inch?

\newline

\text{in}

^{3}

What is the volume of a cylinder with a height of

11

7

\text{in}

and a base with a diameter of

10

6

\text{in}

, to the nearest tenth of a cubic inch?

\newline

\text{in}

^{3}

Find the volume of a rectangular prism with a length of

12.2

\mathrm{in}

14

\text{in}

and a height of

7.1

\mathrm{in}

, to the nearest tenth of a cubic inch.

\newline

\text{in}

^{3}

Slow and steady wins the race. The leatherback sea turtle is the fastest known reptile, with a maximum speed of

21

92

miles per hour (

\mathrm{mph})

\newline

Which of the following equations, where

d

is distance in miles and

t

is time in hours, represents a speed that is less than that of the leatherback sea turtle?

\newline

Choose all answers that apply:

\newline

d=2.192 t

\newline

d=20 t

\newline

d=22 t

\newline

d=30 t

6

\newline

1

\newline

A square pyramid has a volume of

484 \mathrm{~cm}^{3}

and a height of

12 \mathrm{~cm}

. Find the length.

\newline

11 \mathrm{~cm}

\newline

40.3 \mathrm{~cm}

\newline

121 \mathrm{~cm}

The volume of a cylinder is

54 \pi

cubic inches and the height is

6

inches. Find the radius.

\newline

3 \mathrm{~cm}

\newline

9 \mathrm{~cm}

\newline

3.14 \mathrm{~cm}

\newline

1 \mathrm{~cm}

What is the volume of a square-based pyramid with base side length of

8

inches and a height of

12

inches? Write your answer in the box provided.

\newline

\square

A new car is purchased for

23

700

dollars. The value of the car depreciates at a rate of

2 \%

per year. Which equation represents the value of the car after

2

\newline

V=23,700(1-0.02)^{2}

\newline

V=23,700(1+0.02)^{2}

\newline

V=23,700(0.8)^{2}

\newline

V=23,700(1.02)^{2}

A new car is purchased for

29

900

dollars. The value of the car depreciates at a rate of

2.7 \%

per year. Which equation represents the value of the car after

4

\newline

V=29,900(1-0.027)(1-0.027)(1-0.027)

\newline

V=29,900(0.973)^{4}

\newline

V=29,900(1.027)^{4}

\newline

V=29,900(1+0.027)^{4}

The Great Pyramid of Giza was constructed as a regular pyramid with a square base. It was built with an approximate volume of

2,592,276

cubic meters and a height of

146

5

meters. What was the length of one side of its base, to the nearest meter?

\newline

1

73

\newline

3

133

\newline

2

77

\newline

4

230

36a + 28.3w = 100

\newline

A bottle contains

100

milliliters of a solution of alcohol and water at room temperature. The equation shows the possible amounts of alcohol,

a

w

, in ounces. What is the volume of

1

ounce of alcohol at room temperature in milliliters?

\newline

1

\newline

0.03

\newline

2.8

\newline

28.3

\newline

36

V=\pi r^{2}h

\newline

The formula gives the volume

V

of a right circular cylinder with radius

r

h

. What is the volume, in cubic centimeters, of a right circular cylinder with a radius of

2

centimeters and a height of

20

\newline

1

\newline

40 \pi

\newline

80 \pi

\newline

400 \pi

\newline

800 \pi

The lengths of the four sides of a quadrilateral (in centimeters) are consecutive even integers. If the perimeter is

84

centimeters, find the value of the longest of the four side lengths.

\newline

Answer: centimeters

A rectangular prism has a length of

20

\text{in}

2

\text{in}

, and a width of

17 \mathrm{in}

. What is its volume, in cubic in?

\newline

V= \square

\text{in}

^{3}

Find the volume of a pyramid with a square base, where the side length of the base is

17.7 \mathrm{~m}

and the height of the pyramid is

9.4 \mathrm{~m}

. Round your answer to the nearest tenth of a cubic meter.

\newline

\mathrm{m}^{3}

Find the volume of a pyramid with a square base, where the area of the base is

19.9 \mathrm{~m}^{2}

and the height of the pyramid is

21.5 \mathrm{~m}

. Round your answer to the nearest tenth of a cubic meter.

\newline

\mathrm{m}^{3}

Find the volume of a pyramid with a square base, where the area of the base is

18.9 \mathrm{~m}^{2}

and the height of the pyramid is

7.6 \mathrm{~m}

. Round your answer to the nearest tenth of a cubic meter.

\newline

\mathrm{m}^{3}

Find the volume of a pyramid with a square base, where the perimeter of the base is

12

3

in and the height of the pyramid is

8.9 \mathrm{in}

. Round your answer to the nearest tenth of a cubic inch.

\newline

^{3}

Find the volume of a pyramid with a square base, where the perimeter of the base is

16.6 \mathrm{~m}

and the height of the pyramid is

18.1 \mathrm{~m}

. Round your answer to the nearest tenth of a cubic meter.

\newline

\mathrm{m}^{3}

Find the volume of a pyramid with a square base, where the area of the base is

17.9 \mathrm{~m}^{2}

and the height of the pyramid is

25.6 \mathrm{~m}

. Round your answer to the nearest tenth of a cubic meter.

\newline

\mathrm{m}^{3}

Find the volume of a pyramid with a square base, where the side length of the base is

6

5

in and the height of the pyramid is

3

8

in. Round your answer to the nearest tenth of a cubic inch.

\newline

^{3}

Find the volume of a pyramid with a square base, where the area of the base is

15.4 \mathrm{~m}^{2}

and the height of the pyramid is

15.6 \mathrm{~m}

. Round your answer to the nearest tenth of a cubic meter.

\newline

\mathrm{m}^{3}

A cylinder has a base diameter of

12 \mathrm{~m}

and a height of

18 \mathrm{~m}

. What is its volume in cubic

\mathrm{m}

, to the nearest tenths place?

\newline

\newline

V=

\mathrm{m}^{3}

What is the volume of a hemisphere with a diameter of

51.2 \mathrm{ft}

, rounded to the nearest tenth of a cubic foot?

\newline

\mathrm{ft}^{3}

What is the volume, in cubic

\mathrm{cm}

, of a rectangular prism with a height of

4 \mathrm{~cm}

4 \mathrm{~cm}

, and a length of

10 \mathrm{~cm}