Surface Area of Pyramids and Cones Worksheet

**Page 4**

31.

What is the slant height of the pyramid, if $h$ is the height of a pyramid standing on a square base of side $a$ units?

a. | √ (4 $h$ ^{2} + $a$^{2})/2 units | ||

b. | √ (2 $h$ ^{2} + $a$^{2})/2 units | ||

c. | (2 $h$ ^{2} + $a$^{2}) units | ||

d. | √ (4 $h$ ^{2} + 2 $a$^{2})/2 units |

Base of the pyramid is a square.

Length of each side of a square =

Slant height of the pyramid = EG

From the figure, EFG is a right triangle.

According to the Pythagoras theorem EG

[Formula.]

FG is parallel to AB and length of FG =

EG

EG

[Substitute the values.]

EG

[Simplify (a/2

EG

[Add.]

√EG

[Take square root on both sides.]

EG = √ (4

[Simplify.]

The slant height of the pyramid with a square base = √ (4

Correct answer : (1)

32.

Perpendicular distance from the base to the opposite vertex is called __________.

a. | Base | ||

b. | Either height or slant height | ||

c. | Slant height | ||

d. | Height |

Correct answer : (4)

33.

Perpendicular distance from the edge of the base to the opposite vertex of a pyramid is called _________________.

a. | Slant height | ||

b. | Height | ||

c. | Base | ||

d. | None of the above |

Correct answer : (1)

34.

Laura distributed paper hats to children on the Christmas eve. The hats are in the shape of a cone with a base radius of 6 cm. and a slant height of 17 cm. Find the surface area of the paper used to make each hat. [Use π = 3.14.]

a. | 102 cm ^{2} | ||

b. | 160.14 cm ^{2} | ||

c. | 320.28 cm ^{2} | ||

d. | 336.58 cm ^{2} |

Curved surface area of the hat = π

[Formula.]

= π × 6 × 17

[Substitute the values.]

= 102π

[Multiply.]

= 102 × 3.14

[Substitute the value of π = 3.14.]

= 320.28 cm.

So, the surface area of the paper used to make a hat = 320.28 cm.

Correct answer : (3)

35.

A circular cone is 6 in. high. The radius of the base is 8 in. What is the curved surface area of the cone?

a. | 251.2 in. ^{2} | ||

b. | 257.2 in. ^{2} | ||

c. | 259.8 in. ^{2} | ||

d. | 245.2 in. ^{2} |

Slant height of the cone =

[Formula.]

=

[Substitute the values.]

=

[Substitute the values of 6

=

[Add.]

= 10

[Simplify.]

Slant height of the cone = 10 in.

Curved surface area of the cone =

[Formula.]

= 3.14 × 8 × 10

[Substitute the values.]

= 251.2 in.

The curved surface area of the cone is 251.2 in.

Correct answer : (1)

36.

The diameter of an ice cream cone is 4 cm. and the slant height is 9 cm. What is the surface area of the cone? [Use π = 3.14.]

a. | 65.08 cm ^{2} | ||

b. | 75.48 cm ^{2} | ||

c. | 69.08 cm ^{2} | ||

d. | 73.08 cm ^{2} |

Radius of an ice cream cone,

[Substitute diameter = 4.]

Surface area of the cone = π

[Formula.]

= π × 2 × 9 + π × 2

[Substitute the values.]

= 18π + 4π

= 22π

[Add.]

= 22 × 3.14

[Substitute the value of π = 3.14.]

= 69.08

[Multiply.]

The surface area of the cone is 69.08 cm.

Correct answer : (3)

37.

The circumference of the base of a conical tent is 25.12 m. and its slant height is 8 m. Find the area of the canvas used in making the tent.[Use $\pi $ = 3.14.]

a. | 102.48 m ^{2} | ||

b. | 106.48 m ^{2} | ||

c. | 98.48 m ^{2} | ||

d. | 100.48 m ^{2} |

Circumference of the conical tent = 2

2 x 3.14 x

[Substitute the value of

6.28

[Multiply 2 with 3.14.]

[Divide each side by 6.28.]

[Simplify.]

Lateral area of the tent =

[Formula.]

= 3.14 x 4 x 8

[Substitute the values.]

= 100.48 m.

[Multiply.]

So, area of the canvas required is 100.48 m.

Correct answer : (4)

38.

What is the slant height of the cone, if its lateral area is 720 ft^{2} and its radius is 12 ft? (Round the answer to the nearest hundredth) [Use π = 3.14.]

a. | 17.11 ft | ||

b. | 19.11 ft | ||

c. | 21.11 ft | ||

d. | None of the above |

Radius of the cone = 12 ft

π x 12 x

[Substitute the value of

(π x 12 x

[Divide each side by 12.]

π

[Simplify.]

3.14 x

[Substitute π = 3.14.]

(3.14 x

[Divide each side 3.14.]

[Simplify.]

The slant height of the cone is 19.11 ft.

Correct answer : (2)

39.

The height of a cone is 16 in. and its diameter is 24 in. What is the slant height of the cone?

a. | 22 in. | ||

b. | 16 in. | ||

c. | 18 in. | ||

d. | 20 in. |

Radius of the cone,

The radius of the cone, height and the slant height form a right triangle.

So, slant height of the cone = √(

[Apply Pythagorean theorem.]

= √(16

[Substitute the values.]

= √(256 + 144)

[Substitute the values of 16

= √400

[Add.]

= 20 in.

[Simplify.]

The slant height of the cone = 20 in.

Correct answer : (4)

40.

The curved surface area of a cone is 2307.90 mm.^{2} and the radius of the base of the cone is 21 mm. What is its height? [Use π = 3.14.]

a. | 30 mm | ||

b. | 33 mm | ||

c. | 28 mm | ||

d. | 23 mm |

Substitute the

π x 21 x

(π x 21 x

[Divide each side by 21.]

π x

[Simplify.]

3.14 x

[Substitute π = 3.14.]

(3.14 x

[Divide each side by 3.14.]

[Simplify.]

Slant height of the cone = 35 mm.

Let

Slant height of the cone = √(

[Formula.]

35 = √(

[Substitute the values.]

35

[Squaring both sides.]

1225 =

[Substitute the values of 35

1225 - 441 =

[Subtract 441 from each side.]

784 =

[Simplify.]

√784 = √

[Square on both the sides.]

28 =

[Simplify.]

The height of the cone = 28 mm.

Correct answer : (3)