Surface Area of Pyramids and Cones Worksheet

**Page 3**

21.

The base area of a cone is 452.16 cm.^{2} and its height is 16 cm. What is the surface area of the cone?

a. | 1205.76 cm ^{2} | ||

b. | 1215.76 cm ^{2} | ||

c. | 1226.41 cm ^{2} | ||

d. | 1195.31 cm ^{2} |

3.14 ×

[Substitute the value of

[Divide each side by 3.14.]

[Simplify.]

[Taking square root on both sides.]

[Simplify.]

Slant height of the cone =

[Formula.]

=

[Substitute the values.]

=

[Substitute the values of 12

=

[Add.]

= 20 cm

[Simplify.]

Slant height of the cone = 20 cm

Surface area of the cone =

[Formula.]

= 3.14 × 12 × 20 + 3.14 × 12

[Substitute the values.]

= 753.60 + 452.16

[Multiply.]

= 1205.76

[Add.]

The surface area of the cone = 1205.76 cm

Correct answer : (1)

22.

Find the surface area of a square pyramid. [$b$ = 5 yd; $h$ = 20 yd.]

a. | 225 yd ^{2} | ||

b. | 224 yd ^{2} | ||

c. | 220 yd ^{2} | ||

d. | 200 yd ^{2} |

[Since a square pyramid has 4 triangles and one square.]

=

[Formula.]

= 5 × 5 + 4 ×

[Substitute the values.]

= 25 + 200 = 225 yd

[Simplify.]

Therefore, the surface area of the square pyramid is 225 yd

Correct answer : (1)

23.

Find the surface area of the cone to the nearest ten $\mathrm{ft}$^{2}.

($d$ = 20 ft, $l$ = 39 ft)

($d$ = 20 ft, $l$ = 39 ft)

a. | 1539 $\mathrm{ft}$ ^{2} | ||

b. | 1,540 $\mathrm{ft}$ ^{2} | ||

c. | 490 $\mathrm{ft}$ ^{2} | ||

d. | 1539.09 $\mathrm{ft}$ ^{2} |

The surface area of a cone = π

[Formula.]

= π × 10

[Substitute the values.]

= 100 π + 390 π

[Simplify.]

= 490 π

= 1539.09 = 1540

[To the nearest ten.]

The surface area of a cone is 1539.09 and to the nearest ten is1540

Correct answer : (2)

24.

The surface area of a square pyramid is given by 540 cm.^{2} and the side of the square is 10 cm. Find the slant height of the square pyramid.

a. | 20 cm | ||

b. | 23 cm | ||

c. | 22 cm | ||

d. | 21 cm |

[Formula.]

Area of the square = s × s = 10 × 10 = 100 cm.

[Substitute.]

Area of the triangle =

[Substitute.]

540 = 100 + 4 ×

540 = 100 + 4 × 5h

[Simplify.]

440 = 20h

[Subtract 100 from both the sides.]

h =

[Divide by 20 on both the sides.]

So, the slant height of the square pyramid is 22 cm.

Correct answer : (3)

25.

The slant height of a strawberry cone is 5 in. and the diameter is 2.3 in. What is the total surface area of the strawberry cone? Let $\pi $ = 3.

a. | 22.21 in ^{2}. | ||

b. | 22 in ^{2}. | ||

c. | 21.21 in ^{2}. | ||

d. | 21 in ^{2}. |

radius =

The surface area of the strawberry cone = π

[Formula.]

= 3 × 1.15 × 1.15 + 3 × 1.15 × 5

[Substitute.]

= 3.96 + 17.25 = 21.21 in.

The surface area of the strawberry cone is 21.21 in.

Correct answer : (3)

26.

The curved surface area of a cone is 169.56 cm^{2} and its slant height is 54 cm. Find the total surface area of the cone. (Round the answer to the nearest hundredth unit.)

a. | 179.1 cm ^{2} | ||

b. | 172.7 cm ^{2} | ||

c. | 169.56 cm ^{2} | ||

d. | 223.56 cm ^{2} |

[Formula.]

Curved surface area of a cone = 169.56 cm

[From the steps-1 and 2.]

[Substitute the value of

[Divide each side by 54.]

π ×

[Rounding the value.]

Total surface area of the cone = π

[Formula.]

= 169.56 + π × (1)

[Substitute the value of

= 172.7

[Simplify.]

The total surface area of the cone = 172.7 cm

Correct answer : (2)

27.

What is the surface area of a pyramid?

a. | Twice the lateral area of the pyramid + base area of the pyramid | ||

b. | Lateral area of the pyramid + base area of the pyramid | ||

c. | Lateral area of the pyramid + twice the base area of the pyramid | ||

d. | None of the above |

Pyramids have only one base.

Surface area of a pyramid = lateral area of the pyramid + base area of the pyramid.

Correct answer : (2)

28.

The total surface area of a cone is 60 in.^{2} If its slant height is four times the radius, then what is the base diameter of the cone? [Use $\pi $ = 3.]

a. | 7 in. | ||

b. | 8 in. | ||

c. | 4 in. | ||

d. | 10 |

Slant height

3 ×

[Substitute

12

[Multiply.]

15

[Add.]

[Divide each side by 15.]

[Simplify.]

[Take square root on both sides.]

[Simplify.]

Base radius of the cone = 2 in.

Base diameter of the cone = 2 × radius = 2 × 2 = 4 in.

Correct answer : (3)

29.

A circular cone with a base radius of 1 ft has a surface area of 15.7 ft^{2}. What is its slant height?

a. | 14 ft | ||

b. | 9 ft | ||

c. | 24 ft | ||

d. | 4 ft |

3.14 x 1 x

[Substitute the values of

3.14

[Multiply.]

3.14

[Subtract 3.14 from each side.]

3.14

[Simplify.]

[Divide each side by 3.14.]

The slant height of the cone is 4 ft .

Correct answer : (4)

30.

Find the surface area of the rectangular pyramid.

a. | 428 m ^{2} | ||

b. | 564 m ^{2} | ||

c. | 550 m ^{2} | ||

d. | 496 m ^{2} |

Area of the lateral face along the length of the rectangle

[Lateral face is a triangle with base 18 m and height 13 m.]

Area of the lateral face along the width of the rectangle

[Lateral face is a triangle with base 10 m and height 15 m.]

Surface area of the rectangular pyramid

[Formula.]

= base area + 2 × area of lateral face along length of the base rectangle + 2 × area of lateral face along the width of the base rectangle

[Substitute the values.]

= 180 + 234 + 150

[Multiply.]

= 564

[Add.]

The surface area of the rectangular pyramid is 564 m

Correct answer : (2)