Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 38

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Weekly Quiz Competition

Question 1
1 / -0

Find the slant height of a frustum cone whose top radius is 5 m and bottom radius is 12 m. The height of the cone is 24 m.

A
25 m

B
23 m

C
20 m

D
24 m

Solution

Slant height, $$L^2 = h^2 + (R - r)^2$$
$$L^2 = {24}^2 + (12 - 5)^2$$
$$L^2 = 576 + 49$$
$$L^2 = 625$$
Squaring on both sides, we get
L = 25 m
Question 2
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 3
1 / -0

The larger radius of a frustum cone is thrice the smaller radius which is 12 m. The slant height of the cone is 120 m. What is the surface area? (Use $$\pi$$ = 3.14).

A
22,608 m$$^2$$

B
21,608 m$$^2$$

C
20,608 m$$^2$$

D
23,608 m$$^2$$

Solution

Surface area of a frustum of cone = $$\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
Larger radius = 3 $$\times$$ smaller radius $$\Rightarrow$$ 3 $$\times$$ 12 = 36m
Smaller radius = 12 m
s = 120 m
SA = $$\pi$$(12 + 36)120 + $$\pi$$12$$^2$$ + $$\pi$$36$$^2$$
= $$\pi$$(48)*120 + 144$$\pi$$ + 1,296$$\pi$$
= 3.14 $$\times$$ (5,760 + 144 + 1,296)
= 3.14 $$\times$$ 7,200
= 22,608 m$$^2$$
Question 4
1 / -0

The larger radius of a frustum cone is double the smaller radius which is 12 in. The slant height of the cone is 40 in. What is the surface area? (Use $$\pi$$ = 3.14).

A
6,182.4 in$$^2$$

B
6,782.4 in$$^2$$

C
6,,682.4 in$$^2$$

D
6,582.4 in$$^2$$

Solution

Surface area of a frustum of cone = $$\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
Larger radius = 2 $$\times$$ smaller radius$$\Rightarrow$$ 2 $$\times$$ 12 = 24 in
Smaller radius = 12 in
s = 40 in
SA = $$\pi$$(12 + 24)40 + $$\pi$$12$$^2$$ + $$\pi$$24$$^2$$
= $$\pi$$(36)40 + 144$$\pi$$ + 576$$\pi$$
= 3.14 $$\times$$ (1,440 + 144 + 576)
= 3.14 $$\times$$ 2,160
= 6,782.4 in$$^2$$
Question 5
1 / -0

The smaller diameter of a frustum cone is thrice the larger radius which is 4 in. The slant height of the cone is 13 in. What is the surface area? (Use $$\pi$$ = 3).

A
2,768 in$$^2$$

B
2,868 in$$^2$$

C
2,668 in$$^2$$

D
2,568 in$$^2$$

Solution

Surface area of a frustum of cone = $$\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
Larger radius = 4 in
Smaller diameter = 3$$\times$$ larger radius $$\Rightarrow$$ 3 $$\times$$ 4 =12 in
Smaller radius = 24 in
s = 13 in
SA = $$\pi$$(24 + 4)13 + $$\pi$$24$$^2$$ + $$\pi$$4$$^2$$
= $$\pi$$(28)13 + 576$$\pi$$ + 16$$\pi$$
= 3 $$\times$$ (364 + 576 + 16)
= 3 $$\times$$ 956
= 2,868 in$$^2$$
Question 6
1 / -0

Calculate the total surface area of frustum cone given below :

A
57 $$\pi cm^2$$

B
67 $$\pi cm^2$$

C
77 $$\pi cm^2$$

D
87 $$\pi cm^2$$

Solution

Total surface area = $$\pi (R+r)s + \pi R^2 + \pi r^2$$
= $$\pi (4 + 1)10 + \pi 4^2 + \pi 1^2$$
= $$50 \pi + 16 \pi + \pi$$
= $$67 \pi cm^2$$
Question 7
1 / -0

Find the slant height of a frustum cone whose top radius is 12 cm and bottom radius is 7 cm. The height of the cone is 12 cm.

A
15 cm

B
13 cm

C
10 cm

D
14 cm

Solution

Formula of slant height is given by $$L^2 = h^2 + (R - r)^2$$
Given $$h = 12\ cm , R = 12\ cm, r = 7 \ cm$$
by substituting the values we get:
$$L^2 = {12}^2 + (12 - 7)^2$$
$$L^2 = 144 + 25$$
$$L^2 = 169$$
$$L = 13 \ cm$$
Question 8
1 / -0

Calculate the total surface area of a frustum cone:
Given D = 2 cm, d = 1 cm, s = 10 cm.

A
109.9 $${cm}^2$$

B
255.48 $${cm}^2$$

C
235.48 $${cm}^2$$

D
215.48 $${cm}^2$$

Solution

Total surface area = $$\pi (R+ r)s + \pi R^2 + \pi r^2$$
Diameter = radius $$\times 2$$
Radius, R = 1 cm, r = 0.5 cm
= 3.14 (1 + 0.5)*10 + π* $$1^2$$ + π* $$0.5^2$$
= $$3.14 \times 15 + 3.14 \times 1 + 0.25 \times 3.14$$
= $$ 51.025 {cm}^2$$
Question 9
1 / -0

The curved surface area of a frustum cone is 250 m$$^2$$. The larger circle area is 120 m$$^2$$. The total surface area is 1000 m$$^2$$. Find the smaller circle area of a cone.

A
630 m$$^2$$

B
620 m$$^2$$

C
610 m$$^2$$

D
600 m$$^2$$

Solution

Curved surface area of a frustum cone $$=\pi$$(r + R)s $$\Rightarrow$$ 250 m$$^2$$
Surface area of a frustum of cone = $$\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$ $$\Rightarrow$$ 1000 m$$^2$$
Larger circle area = $$\pi$$R$$^2$$ $$\Rightarrow$$ 120 m$$^2$$
Smaller circle area = $$\pi$$r$$^2$$ $$\Rightarrow$$ ?
Therefore,
SA = $$\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
100 = 250 + Area of smaller circle + 120
1000 = 250
120 = Area of smaller circle
Area of smaller circle of a frustum cone = 630 m$$^2$$
Question 10
1 / -0

Calculate the curved surface area of a frustum cone given below :

A
125.6 $$in^2$$

B
225.6 $$in^2$$

C
325.6 $$in^2$$

D
425.6 $$in^2$$

Solution

Curved surface area = $$ \pi (R + r) l $$
= $$\pi (3+1)\times 10$$
= $$3.14 \times 4 \times 10$$
= 125.6 $$in^2$$

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Re-Attempt Weekly Quiz Competition

Surface Areas and Volumes Test - 38

Result

Surface Areas and Volumes Test - 38

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SHARING IS CARING

Question 1

25 m

23 m

20 m

24 m

Solution

Question 2

83,228.57 m$$^2$$

82,228.57 m$$^2$$

84,228.57 m$$^2$$

81,228.57 m$$^2$$

Solution

Question 3

22,608 m$$^2$$

21,608 m$$^2$$

20,608 m$$^2$$

23,608 m$$^2$$

Solution

Question 4

6,182.4 in$$^2$$

6,782.4 in$$^2$$

6,,682.4 in$$^2$$

6,582.4 in$$^2$$

Solution

Question 5

2,768 in$$^2$$

2,868 in$$^2$$

2,668 in$$^2$$

2,568 in$$^2$$

Solution

Question 6

57 $$\pi cm^2$$

67 $$\pi cm^2$$

77 $$\pi cm^2$$

87 $$\pi cm^2$$

Solution

Question 7

15 cm

13 cm

10 cm

14 cm

Solution

Question 8

109.9 $${cm}^2$$

255.48 $${cm}^2$$

235.48 $${cm}^2$$

215.48 $${cm}^2$$

Solution

Question 9

630 m$$^2$$

620 m$$^2$$

610 m$$^2$$

600 m$$^2$$

Solution

Question 10

125.6 $$in^2$$

225.6 $$in^2$$

325.6 $$in^2$$

425.6 $$in^2$$

Solution

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