Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 37

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Weekly Quiz Competition

Question 1
1 / -0

Find the surface area of a frustum of cone, whose larger and smaller radius is 1.5 cm and 0.2 cm. The slant height of the cone is 2.5 cm. (Use $$\pi$$ = 3.14)

A
20.666 cm$$^2$$

B
21.666 cm$$^2$$

C
22.666 cm$$^2$$

D
23.666 cm$$^2$$

Solution

Surface area of a frustum of cone = $$\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
R = 1.5 cm, r = 0.2 cm, s = 2.5 cm
SA = $$\pi$$(0.2 + 1.5)2.5 +$$\pi$$0.2$$^2$$ + $$\pi$$1.5$$^2$$
= $$\pi$$(1.7)2.5 + 0.4$$\pi$$ + 2.25$$\pi$$
= 3.14 $$\times$$ (4.25 + 0.4 + 2.25)
= 3.14 $$\times$$ 6.9
= 21.666 cm$$^2$$
Question 2
1 / -0

Find the surface area of a frustum of cone, whose larger and smaller radius is 25 cm and 12 cm. The slant height of the cone is 30 cm. (Use $$\pi$$ = 3.14)

A
5,600.96 cm$$^2$$

B
5,700.96 cm$$^2$$

C
5,800.96 cm$$^2$$

D
5,900.96 cm$$^2$$

Solution

Surface area of a frustum of cone $$=\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
R = 25 cm, r = 12 cm, s = 30 cm
SA = $$\pi$$(12 + 25)30 + $$\pi$$12$$^2$$ + $$\pi$$25$$^2$$
= $$\pi$$(37)30 + 144$$\pi$$ + 625$$\pi$$
= 3.14 $$\times$$ (1,110 + 144 + 625)
= 3.14 $$\times$$ 1,879
= 5,900.96 cm$$^2$$
Question 3
1 / -0

The larger and smaller diameter of a cone is 35 m and 15 m. The slant height of the cone is 210 m. What is the surface area of a frustum of cone? (Use $$\pi$$ = 22/7).

A
83,228.57 m$$^2$$

B
82,228.57 m$$^2$$

C
84,228.57 m$$^2$$

D
81,228.57 m$$^2$$

Solution

Surface area of a frustum of cone = $$\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
Diameter = radius/2
Radius, R = 70 m, r = 30 m, slant height, s = 210 m
SA = $$\pi$$(70 + 30)210 + $$\pi$$30$$^2$$ + $$\pi$$70$$^2$$
= $$\pi$$(100)210 + 900$$\pi$$ + 4900$$\pi$$
= 22/7 $$\times$$ (21000 + 900 + 4900)
= 22/7 $$\times$$ 26,800
= 84,228.57 m$$^2$$
Question 4
1 / -0

The larger and smaller diameter of a cone is 14 m and 5 m. The slant height of the cone is 100 m. What is the surface area of a frustum of cone? (Use $$\pi$$ = 3).

A
13,052 m$$^2$$

B
14,052 m$$^2$$

C
15,052 m$$^2$$

D
16,052 m$$^2$$

Solution

Surface area of a frustum of cone = $$\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
SA = $$\pi$$(28 + 10)100 + $$\pi$$10$$^2$$ + $$\pi$$28$$^2$$
= $$\pi$$(38)100 + 100$$\pi$$ + 784$$\pi$$
= 3 $$\times$$ (3800 + 100 + 784)
= 3 $$\times$$ 4,684
= 14,052 m$$^2$$
Question 5
1 / -0

Find the surface area of a frustum of cone, whose larger and smaller radius is 50 m and 20 m. The slant height of the cone is 100 m. (Use $$\pi$$ = 3)

A
29,700 m$$^2$$

B
28,700 m$$^2$$

C
27,700 m$$^2$$

D
26,700 m$$^2$$

Solution

Surface area of a frustum of cone = $$\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
R = 50 m, r = 20 m, s = 100 m
SA = $$\pi$$(20 + 50)100 +$$\pi$$20$$^2$$ + $$\pi$$50$$^2$$
= $$\pi$$(70)100 + 400$$\pi$$ + 2500$$\pi$$
= 3$$\times$$ (7000 + 400 + 2500)
= 3 $$\times$$ 9,900
= 29,700 m$$^2$$
Question 6
1 / -0

The circumference of lower and upper bases of the frustum cone is 11 and 23 m. The slant height is 12 m. What is the curved surface area ?

A
204 $$m^2$$

B
300 $$m^2$$

C
200 $$m^2$$

D
100 $$m^2$$

Solution

Curved surface area of the frustum cone
= $$\displaystyle \frac{1}{2}(2\pi R+2\pi r)l$$
= $$\displaystyle \frac{1}{2} (11 + 23) \times 12$$
= $$34 \times 6$$
= 204 $$m^2$$
Question 7
1 / -0

Find the slant height of a frustum cone whose top radius is 12 m and bottom radius is 10 m. The height of the cone is 13 m.

A
13.15 m

B
12.15 m

C
10.15 m

D
14.25 m

Solution

For a frustum of cone, if $$h$$ is the height, $$r_1$$ is the base radius, $$r_2$$ is the top radius, slant height is $$l$$
Then slant height, $$l^2 = h^2 + (r_1 - r_2)^2$$
$$\Rightarrow l^2 = {13}^2 + (12 - 10)^2$$
$$\Rightarrow l^2 = 169 + 4$$
$$\Rightarrow l^2 = 173$$
$$\Rightarrow l = 13.15 m$$
Question 8
1 / -0

The larger diameter of a frustum cone is double the smaller diameter which is 6 cm. The slant height of the cone is 20 cm. What is the surface area? (Use $$\pi$$ = 3.14).

A
4,721.6 cm$$^2$$

B
4,821.6 cm$$^2$$

C
4,621.6 cm$$^2$$

D
4,521.6 cm$$^2$$

Solution

Surface area of a frustum of cone = $$\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
Larger diameter = 2 $$\times$$ smaller diameter $$\Rightarrow$$ 2 $$\times$$ 6 =12 cm
Smaller diameter = 6cm
Diameter = radius/2
Radius, R = 24 cm, r = 12 cm
s = 20 cm
SA = $$\pi$$(12 + 24)20 + $$\pi$$12$$^2$$ + $$\pi$$24$$^2$$
= $$\pi$$(36)20 + 144$$\pi$$ + 576$$\pi$$
= 3.14 $$\times$$ (720+ 144 + 576)
= 3.14 $$\times$$ 1,440
= 4,521.6 cm$$^2$$
Question 9
1 / -0

Find the slant height of a frustum cone whose top radius is 14 in and bottom radius is 2 in. The height of the cone is 9 in.

A
15 in

B
12 in

C
10 in

D
14 in

Solution

Slant height, $$L^2 = h^2 + (R - r)^2$$
$$L^2 = {9}^2 + (14 - 2)^2$$
$$L^2 = 81 + 144$$
$$L^2 = 225$$
Squaring on both sides, we get
L = 15 in
Question 10
1 / -0

Find the slant height of a frustum cone whose top radius is 10 ft and bottom radius is 4 ft. The height of the cone is 8 ft.

A
15 ft

B
12 ft

C
10 ft

D
14 ft

Solution

Slant height, $$L^2 = h^2 + (R - r)^2$$
$$L^2 = {8}^2 + (10 - 4)^2$$
$$L^2 = 64 + 36$$
$$L^2 = 100$$
Squaring on both sides, we get
L = 10 ft

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Surface Areas and Volumes Test - 37

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Surface Areas and Volumes Test - 37

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Question 1

20.666 cm$$^2$$

21.666 cm$$^2$$

22.666 cm$$^2$$

23.666 cm$$^2$$

Solution

Question 2

5,600.96 cm$$^2$$

5,700.96 cm$$^2$$

5,800.96 cm$$^2$$

5,900.96 cm$$^2$$

Solution

Question 3

83,228.57 m$$^2$$

82,228.57 m$$^2$$

84,228.57 m$$^2$$

81,228.57 m$$^2$$

Solution

Question 4

13,052 m$$^2$$

14,052 m$$^2$$

15,052 m$$^2$$

16,052 m$$^2$$

Solution

Question 5

29,700 m$$^2$$

28,700 m$$^2$$

27,700 m$$^2$$

26,700 m$$^2$$

Solution

Question 6

204 $$m^2$$

300 $$m^2$$

200 $$m^2$$

100 $$m^2$$

Solution

Question 7

13.15 m

12.15 m

10.15 m

14.25 m

Solution

Question 8

4,721.6 cm$$^2$$

4,821.6 cm$$^2$$

4,621.6 cm$$^2$$

4,521.6 cm$$^2$$

Solution

Question 9

15 in

12 in

10 in

14 in

Solution

Question 10

15 ft

12 ft

10 ft

14 ft

Solution

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