Surface Area of Pyramids and Cones Worksheet

**Page 6**

51.

What is the base area of a cone with a radius of 8 in. and a height of 28 in.?

a. | 190.09 in. ^{2} | ||

b. | 200.96 in. ^{2} | ||

c. | 211.83 in. ^{2} | ||

d. | 221.83 in. ^{2} |

Base area of the cone =

[Formula.]

= 3.14 × 8

[Substitute the values.]

= 3.14 × 64

[Substitute the value of 8

= 200.96

[Multiply.]

The base area of the cone is 200.96 in.

Correct answer : (2)

52.

The radius and the height of a right circular cone are $\frac{6}{\mathrm{\pi}}$ cm. and $\frac{8}{\mathrm{\pi}}$ cm. respectively. What is the curved surface area of the right circular cone? (Round the answer to the nearest hundredth of a unit.)

a. | 23.21 cm | ||

b. | 19.11 cm | ||

c. | 21.61 cm | ||

d. | 15.11 cm |

Height of the cone =

Slant height of the cone = √ (h

[Formula.]

= √ ((

[Substitute the values.]

= √ (64/π

[Substitute the square values.]

= √ ((64 + 36)/π

[Add fractions.]

= √ (100/π

[Add 64 and 36.]

=

[Simplify.]

Slant height of the cone =

Curved surface area of the right circular cone =

[Formula.]

=

[Substitute the values.]

=

[Multiply.]

=

[Substitute the value of π = 3.14.]

= 19.1082

[Simplify.]

[Round to the nearest hundredths.]

Correct answer : (2)

53.

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

a. | 1216.21 in. ^{2} | ||

b. | 1205.76 in. ^{2} | ||

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

d. | 1195.31 in. ^{2} |

3.14 ×

[Substitute the value of

[Divide each side by 3.14.]

[Simplify.]

[Taking the square root on both sides.]

[Simplify.]

[Formula.]

=

[Substitute the values.]

=

[Substitute the values of 12

=

[Add.]

= 20 in.

[Simplify.]

Slant height of the cone = 20 in.

Surface area of the cone =

= 3.14 × 12 × 20 + 3.14 × 12

= 753.60 + 452.16

= 1205.76

The surface area of the cone is 1205.76 in.

Correct answer : (2)

54.

What is the surface area of the figure?

a. | 742.78 mm ^{2} | ||

b. | 723.56 mm ^{2} | ||

c. | 769.3 mm ^{2} | ||

d. | 722.78 mm ^{2} |

Base radius of the cylinder =

Surface area of the figure = base area + lateral area of the cylinder + lateral area of the cone

[Formula.]

=

=

[Substitute the values.]

= 25

[Multiply.]

= 245

[Add.]

= 245 x 3.14

[Substitute the

= 769.3 mm.

[Multiply.]

The surface area of the figure is 769.3 mm.

Correct answer : (3)

55.

What is the base area of a square pyramid with lateral edge($a$) 15 cm and height($h$) 12 cm?

a. | 81 cm ^{2} | ||

b. | 18 cm ^{2} | ||

c. | 324 cm ^{2} | ||

d. | 162 cm ^{2} |

[Height AB is perpendicular to BC and the lateral edge AC is the hypotenuse.]

BC

[Apply Pythagorean theorem.]

BC

[Substitute height, AB = 12 and lateral edge, AC = 15.]

BC

[Simplify.]

BC

[Subtract 144 from both sides.]

BC =

[Take square root on both sides.]

Diagonal of the square base = 2 × BC

[BC is half the diagonal of the square base.]

= 2 × 9 = 18 cm

[Substitute and multiply.]

Area of a square =

[Formula for the area of a square in terms of the measure of diagonals.]

=

[The diagonals of a square have equal measures. Substitute the values.]

The base area of the square pyramid is 162 cm

Correct answer : (4)

56.

What is the base area of the square pyramid whose lateral edge(b) is 8 cm and the height(a) is 7 cm?

a. | 80 cm ^{2} | ||

b. | 130 cm ^{2} | ||

c. | 30 cm ^{2} | ||

d. | 50 cm ^{2} |

[Height AB is perpendicular to BC and the lateral edge AC is the hypotenuse.]

BC

[Apply Pythagorean theorem.]

BC

[Substitute height, AB = 7 and lateral edge, AC = 8.]

BC

[Simplify.]

BC

[Subtract 49 from both sides.]

BC =

[Take square root on both sides.]

Diagonal of the square base = 2 × BC

[BC is half the diagonal of the square base.]

= 2 ×

[Substitute and multiply.]

Area of a square =

[Formula for the area of a square in terms of the measure of diagonals.]

=

[The diagonals of a square have equal measures. Substitute the values.]

The base area of the square pyramid is

Correct answer : (3)

57.

Find the volume of the rectangular pyramid.

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

b. | 100 cm ^{3} | ||

c. | 160 cm ^{3} | ||

d. | 140 cm ^{3} |

Volume of a rectangular pyramid = (

= (

[Substitute the values.]

=

= 40 cm

[Simplify.]

The volume of the rectangular pyramid is 40 cm

Correct answer : (1)