Surface Area of Pyramids and Cones Worksheet

**Page 5**

41.

The curved surface area of a cone is 292.02 cm.^{2} and its slant height is 93 cm. Find the total surface area of the cone. (Round the answer to the nearest hundredth unit.) [Use π = 3.14.]

a. | 299.16 cm ^{2} | ||

b. | 301.56 cm ^{2} | ||

c. | 295.16 cm ^{2} | ||

d. | 291.16 cm ^{2} |

[Formula.]

Curved surface area of a cone = 292.02 cm.

π

[From the steps 1 and 2.]

π ×

[Substitute the value

[Divide each side by 93.]

π

3.14 ×

[Substitute π = 3.14.]

[Divide each side by 3.14.]

Total surface area of the cone = π

[Formula.]

= 292.02 + 3.14 × 1

[Substitute the value of π and curved surface area.]

= 292.02 + 3.14 × 1

= 292.02 + 3.14

[Simplify.]

= 295.16

[Add.]

The total surface area of the cone = 295.16 cm

Correct answer : (3)

42.

What length of canvas, 4 m. in width is required to make a conical tent 14 m. in diameter and 6.3 m. slant height? Also find the cost of the canvas at the rate of $13 per meter. (Round the answer to the nearest hundredth of a unit.) [Use π = 3.14.]

a. | Length = 30.62 m, cost = $446.06 | ||

b. | Length = 38.62 m, cost = $454.06 | ||

c. | Length = 34.62 m, cost = $454.06 | ||

d. | Length = 34.62 m, cost = $450.06 |

Radius of the tent,

Lateral area of the tent = π

[Formula.]

= 3.14 x 7 x 6.3

[Substitute the values.]

= 138.474 m.

[Multiply.]

Lateral area of the tent = 138.474 m.

Required canvas = lateral area of the tent = 138.474 m.

Width of the canvas = 4 m.

Length of the canvas = area of canvas/width of canvas

=

[Substitute the values.]

= 34.618 m

Length of the canvas = 34.62 m.

Cost of the canvas = $13 per meter.

Total cost of required canvas = 34.62 x 13 = $450.06

The length of the canvas is 34.62 m. and it's total cost is $450.06

Correct answer : (4)

43.

A cone made of paper is 24 in. high and has a radius of 7 in. Find the area of the paper needed to construct the cone. [Use π = 3.14.]

a. | 681.38 in. ^{2} | ||

b. | 703.36 in. ^{2} | ||

c. | 527.52 in. ^{2} | ||

d. | 549.5 in. ^{2} |

Slant height of the tent,

[Formula.]

=

[Substitute the values.]

=

[Substitute the values of 24

=

[Add.]

= 25

[Simplify.]

Slant height of the cone,

Surface area of the cone =

[Formula.]

= (3.14 × 7 × 25) + (3.14 × 7 × 7)

[Substitute the values.]

= 549.5 + 153.86 = 703.36

[Simplify.]

Therefore, 703.36 in.

Correct answer : (2)

44.

You need to paint the outside of the house as shown in the figure. A gallon of paint covers about 400 square feet. How many gallons will you need to buy? (Ignore the areas of window and door.)

a. | 5 gallons | ||

b. | 2.5 gallons | ||

c. | 6 gallons | ||

d. | 4.5 gallons |

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

[Formula.]

Length of the side of the square in each face of the cube = 20 ft

Area of the square = side x side = 20 × 20 = 400 ft

Base of the triangle = 20 ft and its height = 10 ft

Area of the triangle =

Out side area of the house = 4 × 400 + 4 × 100

[Substitute the values in the step 2.]

= 1600 + 400

[Multiply.]

= 2000

[Add.]

Out side area of the house = 2000 ft

A gallon of paint covers the area = 400 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 : (1)

45.

From the two figures shown, which has the larger surface area?

a. | Pyramid | ||

b. | Both cannot be compared | ||

c. | Both cone and pyramid have equal surface areas. | ||

d. | Cone |

Length of each side of the base of the pyramid = diameter of the cone = 10 in.

Radius of the cone = diameter of the cone/2 =

Surface area of the cone =

[Formula.]

= 3.14 x 5 x 13 + 3.14 x 5

[Substitute the values.]

= 204.1 + 78.5

[Multiply.]

= 282.6

[Add.]

Surface area of cone = 282.6 in.

Surface area of the pyramid = base area + 4 x area of triangle

[Formula.]

= (side x side) + 4 x

= (10 x 10) + 4 x

[Substitute the values.]

= 100 + 260

[Multiply.]

= 360

[Add.]

Surface area of the pyramid = 360 in.

So, the pyramid has a larger surface area.

Correct answer : (1)

46.

What length of paper, of width 30 in., will be required to make a hollow cone of radius 12 in. and slant height 45 in.?

a. | 1696 in. | ||

b. | 678.24 in. | ||

c. | 56.52 in. | ||

d. | 18 in. |

Lateral area of the cone =

[Formula.]

= 3.14 x 12 x 45

[Substitute the values.]

= 1695.60 in.

[Multiply.]

The lateral area of the cone = 1695.60 in.

Area of the required paper = lateral area of the cone = 1695.60 in.

Width of the paper = 30 in.

Length of the paper = area of the paper/width of the paper

[Formula.]

=

[Substitute the values.]

= 56.52 in.

[Simplify.]

The length of the paper = 56.52 in.

Correct answer : (3)

47.

The slant height of a cone is 35 in. and its base radius is 28 in. What is its height?

a. | 27 in. | ||

b. | 23 in. | ||

c. | 21 in. | ||

d. | 25 in. |

Let

Slant height = √ (

[Formula.]

35 = √ (

[Substitute the values.]

35

[Squaring both sides.]

1225 =

[Simplify.]

1225 - 784 =

[Subtract 784 from both sides.]

441 =

[Simplify.]

√441 = √h

[Taking square root on both sides.]

21 =

[Simplify.]

The height of the cone = 21 in.

Correct answer : (3)

48.

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

a. | 15 units | ||

b. | 13 units | ||

c. | 19 units | ||

d. | 17 units |

Let

Slant height of the cone (

[Substitute the value of

3

[Multiply.]

3

[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 : (1)

49.

What is the total surface area of the figure?

a. | 188.4 cm ^{2} | ||

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

c. | 216.66 cm ^{2} | ||

d. | 244.92 cm ^{2} |

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

[Formula.]

=

=

[Substitute the values.]

= 9

[Multiply.]

= 60

[Add.]

= 60 x 3.14

[Substitute the value of

= 188.4 cm.

[Multiply.]

The surface area of the figure = 188.4 cm.

Correct answer : (1)

50.

What is the expression for the surface area of a cone, whose slant height is 4 times the radius of its base?

a. | 5$\pi $$r$ ^{2} unit^{2} | ||

b. | 7$\pi $$r$ ^{2} unit^{2} | ||

c. | 6$\pi $$r$ ^{2} unit^{2} | ||

d. | 4$\pi $$r$ ^{2} unit^{2} |

Slant height of the cone = 4 times the radius = 4 x

Surface area of the cone =

[Formula.]

=

[Substitute

= 4

[Multiply.]

= 5

[Add.]

The surface area of the cone is 5

Correct answer : (1)