Volume of Pyramids and Cones Worksheet

**Page 3**

21.

Which of the following statements is/are false?

I. Volume of a cone is one-third of the product of the base area and height.

II. Volume of a cylinder is the product of base area and height.

III. Volume of a cylinder is the sum of its base area and its height.

IV. Volume of a cone is one-fourth the product of its base area and height.

I. Volume of a cone is one-third of the product of the base area and height.

II. Volume of a cylinder is the product of base area and height.

III. Volume of a cylinder is the sum of its base area and its height.

IV. Volume of a cone is one-fourth the product of its base area and height.

a. | II and III only | ||

b. | I and II only | ||

c. | III and IV only | ||

d. | II and IV only |

Volume of a cylinder is the product of base area and height.

Therefore, the statements I and II are true.

Hence, the statements III and IV are false.

Correct answer : (3)

22.

A cone and a cylinder have the same radius and same height. Which of the following is false for the volume of cone and cylinder?

a. | Volume of the cone is lesser than the volume of the cylinder. | ||

b. | Volume of the cone is $\frac{1}{3}$ times the volume of the cylinder. | ||

c. | Volume of the cone is same as the volume of the cylinder. | ||

d. | Volume of the cylinder is 3 times the volume of the cone. |

Volume of the cone =

= 3 × volume of a cone

Volume of a cylinder = base area × height = 3(

Therefore, the statement 'volume of the cone is same as the volume of the cylinder' is false.

Correct answer : (3)

23.

Find the volume of the figure shown, if AB = 8 ft and CO = C′ O = 18 ft.

a. | 94$\pi $ ft ^{3} | ||

b. | 190$\pi $ ft ^{3} | ||

c. | 192$\pi $ ft ^{3} | ||

d. | 96$\pi $ ft ^{3} |

and the height of each cone,

=

The base radius of the cone,

[Substitute diameter = 8 ft.]

= 4 ft

[Divide numerator and denominator by 3.]

Volume of each cone, V =

[Formula.]

=

[Substitute

= 96

[Simplify.]

The volume of the figure = 2 × V

[Since the figure contains two identical cones.]

= 2 × 96

[Substitute, V = 96

= 192

The volume of the figure is 192

Correct answer : (3)

24.

Find the volume of the rectangular pyramid shown.

a. | 140 cm ^{3} | ||

b. | 120 cm ^{3} | ||

c. | 40 cm ^{3} | ||

d. | 100 cm ^{3} |

Volume of a rectangular pyramid =

=

[Substitute the values.]

=

= 40 cm

[Simplify.]

The volume of the rectangular pyramid is 40 cm

Correct answer : (3)

25.

What is the base area of a rectangular pyramid, whose height is 15 cm and volume is 125 cm^{3}?

a. | 10 cm ^{2} | ||

b. | 25 cm ^{2} | ||

c. | 8 cm ^{2} | ||

d. | none of these |

[Volume formula.]

The base area of the rectangular pyramid =

=

[Substitute the values.]

=

[Multiply 3 by 125.]

= 25

[Divide.]

The base area of the rectangular pyramid is 25 cm

Correct answer : (2)

26.

What is the base width of a rectangular pyramid, if its length, height, and volume are 3 cm., 2 cm. , and 12 cm^{3} respectively?

a. | 1 cm | ||

b. | 2 cm | ||

c. | 11 cm | ||

d. | 6 cm |

[Volume formula.]

The base width of the rectangular pyramid =

=

[Substitute the values.]

=

[Simplify.]

= 6

[Divide the numerator and the denominator by 6.]

So, the base width of the rectangular pyramid is 6 cm.

Correct answer : (4)

27.

Find the volume of the rectangular pyramid, whose base length, diagonal of the base and height of the pyramid are 4 cm, 5 cm, and 6 cm respectively.

a. | 70 cm ^{3} | ||

b. | 24 cm ^{3} | ||

c. | 60 cm ^{3} | ||

d. | none of these |

According to the right triangle property, 4

16 +

[Subtract 16 from 25.]

So, the width of the rectangular base = 3 cm.

Volume of the rectangular pyramid = (

= (

[Substitute the values.]

=

[Multiply 4, 3 and 6.]

= 24 cm.

[Divide.]

Volume of the rectangular pyramid is 24 cm.

Correct answer : (2)

28.

What is the base area and volume of the rectangular pyramid whose length, width, and height are 6 cm, 4 cm , and 5 cm respectively?

a. | 24 cm ^{3} and 120 cm^{2} | ||

b. | 24 cm ^{2} and 40 cm^{3} | ||

c. | 24 cm ^{2} and 100 cm^{3} | ||

d. | none of these |

= 6 × 4

[Substitute the values.]

= 24 cm

[Multiply 6 by 4.]

The volume of a rectangular pyramid =

=

[Substitute the values.]

=

[Multiply 24 by 5.]

= 40 cm

[Divide.]

The base area and volume of the rectangular pyramid are 24 cm

Correct answer : (2)

29.

Find the height of the cone whose volume is 480$\pi $ cm.^{3} and base radius is 12 cm.

a. | 20 cm | ||

b. | 13 cm | ||

c. | 10 cm | ||

d. | None of the above |

Volume of the cone,

[Volume formula.]

The height of the cone,

[Substitute

= 10 cm

The height of the cone is 10 cm.

Correct answer : (3)

30.

What is the base radius of a cone, whose volume is 12π ft^{3} and height is 4 ft?

a. | 2 ft | ||

b. | 6 ft | ||

c. | 5 ft | ||

d. | 3 ft |

Volume of the cone, V = (

[Formula.]

[Rewrite the formula.]

=

[Substitute V = 12π and

= 3 ft

[Simplify.]

The base radius of the cone is 3 ft.

Correct answer : (4)