Surface Area of Pyramids and Cones Worksheet

**Page 2**

11.

A circular cone is 12 in. high. The radius of the base is 16 in. What is the lateral surface area of the cone?[Lateral area of cone = π × $r$ × $l$, where $r$, $l$ are the radius and height of the cone]

a. | 28 in. ^{2} | ||

b. | 192 in. ^{2} | ||

c. | 320π in. ^{2} | ||

d. | 328.6 in. ^{2} |

Slant height of the cone =

[Formula.]

=

[Substitute the values.]

=

[Substitute the values of 12

=

[Add.]

= 20

[Simplify.]

Slant height of the cone = 20 in.

lateral surface area of the cone = π

[Formula.]

= π × 16 × 20

[Substitute the values.]

= 320π in.

The lateral surface area of the cone = 320π in.

Correct answer : (3)

12.

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. | 75.48 cm ^{2} | ||

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

c. | 65.08 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 = 69.08 cm

Correct answer : (2)

13.

What length should a 5 m wide canvas be cut in order to make a conical tent of 12 m base diameter and 4.3 m slant height? Find the cost of the tent if the canvas costs $12 per meter. (Round the answer to the nearest hundredth of a unit.)

a. | length = 16.21 m, cost = $194.52 | ||

b. | length = 16.21 m, cost = $198.52 | ||

c. | length = 20.21 m, cost = $198.52 | ||

d. | length = 12.21 m, cost = $190.52 |

Radius of the tent,

Lateral area of the tent =

[Formula.]

= π × 6 × 4.3

[Substitute the values.]

= 81.09 m

[Multiply.]

Lateral area of the tent = 81.09 m

Required canvas = lateral area of the tent = 81.09 m

Width of the canvas = 5 m

Length of the canvas =

=

[Substitute the values.]

= 16.21 m

Length of the canvas = 16.21 m

Cost of the canvas = $12 per meter.

Total cost of required canvas = 16.21 × 12 = $194.52

The length of the canvas is 16.21 m and it's total cost is $194.52

Correct answer : (1)

14.

A paper cone is 60 in. high and has a radius of 25 in.. Find the area of the paper needed to make the cone.

a. | 7135 in. ^{2} | ||

b. | 7087 in. ^{2} | ||

c. | 7065 in. ^{2} | ||

d. | 7100 in. ^{2} |

Slant height of the cone,

[Formula.]

=

[Substitute the values.]

=

[Substitute the values of 60

=

[Add.]

= 65

[Simplify.]

Slant height of the cone,

Surface area of the cone =

[Formula.]

=

[Substitute the values.]

= 90

[Multiply.]

= 2250

[Add.]

= 2250 × π

= 7065 in.

[Multiply.]

The surface area of the cone = 7065 in.

Area of the paper needed = surface area of the cone = 7065 in.

The area of the paper needed to construct the cone is 7065 in.

Correct answer : (3)

15.

You need to paint the out side of the house as shown in the figure. A gallon of paint covers about 1296 square feet. How many gallons will you need to buy? (Ignore the areas of window and door.)[Given $h$ = 18, $b$ = 36.]

a. | 6 gallons | ||

b. | 4 gallons | ||

c. | 3 gallons | ||

d. | 5 gallons |

Out side area of the house = 4 × area of square + 4 × area of triangle

[Formula.]

Length of the side of a square in the cube = 36 ft

Area of the square = side × side = 36 × 36 = 1296 ft

Base of the triangle = 36 ft and its height = 18 ft

Area of the triangle =

Out side area of the house = 4 × 1296 + 4 × 324

[Substitute the values in the step-2.]

= 6480

[Add.]

Out side area of the house = 6480 ft

A gallon of paint covers the area = 1296 ft

Number of gallons required to cover the area of the out side of the house =

The number of gallons required to paint the out side of the house = 5.

Correct answer : (4)

16.

Find the length of paper of width 30 in. required to make a hollow cone of radius 18 in. and slant height 45 in.

a. | 79.85 in. | ||

b. | 89.85 in. | ||

c. | 94.85 in. | ||

d. | 84.85 in. |

Lateral area of the cone =

[Formula.]

= π × 18 × 45

[Substitute the values.]

= 2545.71 in.

[Multiply.]

The lateral area of the cone = 2545.71 in.

Area of the required paper = lateral area of the cone = 2545.71 in.

Width of the paper = 30 in.

Length of the paper =

[Formula.]

=

[Substitute the values.]

= 84.85 in.

[Simplify.]

The length of the paper = 84.85 in.

Correct answer : (4)

17.

The slant height($l$) of a cone is 40 in.. and its base radius($r$) is 32 in.. What is its height?

a. | 44 in. | ||

b. | 24 in. | ||

c. | 34 in. | ||

d. | 54 in. |

Let

Slant height =

[Formula.]

40 =

[Substitute the values.]

40

[Squaring on both sides.]

1600 =

[Simplify.]

1600 - {1024 }=

[Subtract 1024 on both sides.]

576 =

[Simplify.]

[Taking square root on both sides.]

24 =

[Simplify.]

The height of the cone = 24 in.

Correct answer : (2)

18.

The curved surface area of a cone is 75$\pi $ sq. units, whose slant height is 3 times the radius of its base. Find the slant height of the cone.

a. | 13 units | ||

b. | 17 units | ||

c. | 19 units | ||

d. | 15 units |

Let

Slant height of the cone (

[Substitute the value of

3

[Multiply.]

[Divide each side by 3

[Simplify.]

[Taking square root on both sides.]

[Simplify.]

Slant height of the cone = 3

The slant height of the cone = 15 units.

Correct answer : (4)

19.

What is the base area of a cone with radius 7 in. and height 29 in.?

a. | 153.86 in. ^{2} | ||

b. | 164.73 in. ^{2} | ||

c. | 174.73 in. ^{2} | ||

d. | 142.99 in. ^{2} |

Base area of the cone =

[Formula.]

= 3.14 × 7

[Substitute the values.]

= 3.14 × 49

[Substitute the value of 7

= 153.86

[Multiply.]

The base area of the cone = 153.86 in.

Correct answer : (1)

20.

Radius and the height of a right circular cone are $\frac{12}{\mathrm{\pi}}$ in. and $\frac{16}{\mathrm{\pi}}$ in.. What is the curved surface area of the right circular cone? (Round the answer to the nearest hundredth of a unit.)

a. | 276.43 sq. in. | ||

b. | 176.43 sq. in. | ||

c. | 126.43 sq. in. | ||

d. | 76.43 sq. in. |

Height of the cone =

Slant height of the cone =

[Formula.]

=

[Substitute the values.]

=

[Substitute the square values.]

=

[Add fractions.]

=

[Add 144 and 256.]

=

[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.]

= 76.4331

[Simplify.]

[Round to the nearest hundredths.]

Correct answer : (4)