Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 33

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Weekly Quiz Competition

Question 1
1 / -0

Find the curved surface area of a frustum of cone. The slant height is 20 cm, top and bottom radius is 11 and 15 cm respectively. (Use $$\pi$$ = 3)

A
1,860 cm$$^2$$

B
1,760 cm$$^2$$

C
1,660 cm$$^2$$

D
1,560 cm$$^2$$

Solution

Curved surface area $$= \pi\times l \times (R + r) $$
$$= 3 \times 20 \times (11 + 15)$$
$$= 3 \times 20 \times (26)$$
$$= 3 \times 520$$
$$= 1,560 \,cm^2$$
Question 2
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The total surface area of frustum cone is 270 $$in^2$$. The radius of a top cone is 2 and the bottom cone is 2 in. Find the curved surface area of a frustum cone. (Use $$\pi$$ = 3.14).

A
234.88 in

B
244.88 in

C
254.88 in

D
264.88 in

Solution

Total surface area = $$\pi (R+r)s + \pi R^2 + \pi r^2$$
Curved surface area = $$\pi$$(R + r)s
Therefore, 270 = Curved surface area $$+ \pi (2^2 + 2^2)$$
270 = Curved surface area $$+ 3.14 (4 + 4)$$
270 - 25.12 = Curved surface area
Curved surface area = 244.88 in
Question 3
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The slant height of a frustum of a cone is 25 mm, the top and the bottom diameter are 0.2 mm and 0.4 mm respectively. Find the curved surface area of a frustum of cone. (Use $$\pi$$ = 3.14)

A
14.7 mm$$^2$$

B
13.7 mm$$^2$$

C
12.7 mm$$^2$$

D
23.55 mm$$^2$$

Solution

The Curved surface area of frustum of a cone $$= \pi l(R + r) $$
$$\text{Radius} = \dfrac{\text{Diameter}}{2}$$
Top radius $$r=\dfrac{0.2}{2}=0.1$$ mm
Bottom radius $$R=\dfrac{0.4}{2}=0.2$$ mm
Slant height $$l=25$$ mm
Therefore,
Curved surface area $$= 3.14 \times 25(0.2 + 0.1)$$
$$= 3.14 \times 25(0.3)$$
$$= 3.14 \times 7.5$$
$$= 23.55\, mm^2$$
Question 4
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The curved surface area of frustum cone is 360 $$in^2$$. The diameter of a top cone is 12 and the bottom cone is 20 in. Find the slant height. (Use $$\pi$$ = 3.14). Round off your answer to the nearest whole number.

A
7 in

B
3 in

C
4 in

D
5 in

Solution

Curved surface area = $$\pi$$(R + r)s
Diameter = radius $$\times 2$$
Radius, R = 10 in, r = 6 in
360 = $$3.14 \times (10 + 6) \times s$$
360 = $$3.14 \times (16) \times s$$
$$360/3.14 \times 16$$ = s
Slant Height = 7 in
Question 5
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The slant height of a cone is 30 in, top and bottom diameter is 3.5 and 1.6 in respectively. Find the curved surface area of a frustum of cone. (Use $$\pi$$ = 3.14)

A
950.84 in$$^2$$

B
940.84 in$$^2$$

C
960.84 in$$^2$$

D
930.84 in$$^2$$

Solution

Curved surface area $$= \pi*l*(R + r) $$
Diameter = radius/2
Radius, R = 7 in, r = 3.2 in
$$= 3.14 \times 30(7 + 3.2)$$
$$= 3.14 \times 30(10.2)$$
$$= 3.14 \times 306$$
$$=960.84 \,in^2$$
Question 6
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Find the curved surface area of a frustum of a cone. The slant height is $$15 \text{ cm}$$, top and bottom diameter is $$4 \text{ cm}$$ and $$10 \text{ cm}$$ respectively. (Use $$\pi= 3$$)

A
$$1,260 \text{ cm}^2$$

B
$$1,265 \text{ cm}^2$$

C
$$1,660 \text{ cm}^2$$

D
$$1,560\text{ cm}^2$$

Solution

Curved surface area of a frustum of cone is given by $$ \pi l(R + r) .$$
Given $$\Rightarrow$$ $$R = 20 \text{ cm}, \;r = 8 \text{ cm}$$

So,
$$\begin{aligned}{}A& = 3 \times 15(20 + 8)\\& = 45(28)\\& = 1260\text{ cm}^2\end{aligned}$$

Hence, the curved surface area of the frustum of the cone is equal to $$1260\text{ cm}^2.$$
Question 7
1 / -0

Find the curved surface area of a frustum of cone. The slant height is 12 m, top and bottom radius is 2 and 3 m respectively. (Use $$\pi$$ = 3.14)

A
178.4 m$$^2$$

B
188.4 m$$^2$$

C
186.4 m$$^2$$

D
198.4 m$$^2$$

Solution

Curved surface area $$= \pi *l*(R + r) $$
$$= 3.14 \times 12*(2 + 3)$$
$$= 3.14 \times 12*(5)$$
$$= 3.14 \times 60$$
$$= 188.4 \,m^2$$
Question 8
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The area of the curved surface of the frustum of a cone is $$360 m^2$$. The top and base circles have area $$12m^2$$ and $$16 m^2$$ respectively. Find the total surface area.

A
378 $$m^3$$

B
388 $$m^3$$

C
398 $$m^3$$

D
408 $$m^3$$

Solution

Total surface area = $$\pi (R+r)s + A_1 + A_2 $$
Curved surface area = $$\pi (R + r)s \Rightarrow 360 m^2$$
$$A_1 = 16 m, A_2 = 12 m$$
Therefore, Total surface area = 360 + 16 +12
TSA = 388 $$m^3$$
Question 9
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The total surface area of frustum cone is 2,700 $$m^2$$. The diameter of a top cone is 3 and the bottom cone is 4 m. What is the curved surface area of a frustum cone? (Use $$\pi$$ = 3).

A
2,681.25 m

B
2,300.23 mm

C
2,120.25 cm

D
2,300.12 m

Solution

Total surface area = $$\pi (R+r)s + \pi R^2 + \pi r^2$$
Curved surface area = $$\pi(R + r)s$$
Diameter = $$radius \times 2$$
Radius, $$R = 2 m, r = 1.5 m$$
$$\therefore 2700 = \textit{Curved surface area} = \pi (2^2 + 1.5^2)$$
$$2700 = \textit{Curved surface area} = 3 \times (4 + 2.25)$$
$$2700 - 18.75 = \textit{Curved surface area}$$
$$\textbf{Curved surface area} = 2,681.25 m^2$$
Question 10
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The total surface area of frustum cone is 1,500 $$ft^2$$. The radius of a top cone is 10 and the bottom cone is 12 ft. What is the curved surface area of a frustum cone? (Use $$\pi$$ = 3).

A
$$789$$ $$ft^2$$

B
$$765$$ $$ft^2$$

C
$$790$$ $$ft^2$$

D
$$768$$ $$ft^2$$

Solution

Total surface area $$=$$ $$\pi (R+r)s + \pi R^2 + \pi r^2$$

Curved surface area $$=$$ $$\pi$$ $$(R + r)s$$

Therefore, $$1,500$$ $$=$$ Curved surface area $$+ \pi (12^2 + 10^2)$$

$$1,500$$ $$=$$ Curved surface area $$+ (14 3 \times 4 + 100)$$

$$1,500 - 732$$ $$=$$ Curved surface area

Curved surface area $$=$$ $$768$$ $$ft^2$$

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Re-Attempt Weekly Quiz Competition

Surface Areas and Volumes Test - 33

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Surface Areas and Volumes Test - 33

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SHARING IS CARING

Question 1

1,860 cm$$^2$$

1,760 cm$$^2$$

1,660 cm$$^2$$

1,560 cm$$^2$$

Solution

Question 2

234.88 in

244.88 in

254.88 in

264.88 in

Solution

Question 3

14.7 mm$$^2$$

13.7 mm$$^2$$

12.7 mm$$^2$$

23.55 mm$$^2$$

Solution

Question 4

7 in

3 in

4 in

5 in

Solution

Question 5

950.84 in$$^2$$

940.84 in$$^2$$

960.84 in$$^2$$

930.84 in$$^2$$

Solution

Question 6

$$1,260 \text{ cm}^2$$

$$1,265 \text{ cm}^2$$

$$1,660 \text{ cm}^2$$

$$1,560\text{ cm}^2$$

Solution

Question 7

178.4 m$$^2$$

188.4 m$$^2$$

186.4 m$$^2$$

198.4 m$$^2$$

Solution

Question 8

378 $$m^3$$

388 $$m^3$$

398 $$m^3$$

408 $$m^3$$

Solution

Question 9

2,681.25 m

2,300.23 mm

2,120.25 cm

2,300.12 m

Solution

Question 10

$$789$$ $$ft^2$$

$$765$$ $$ft^2$$

$$790$$ $$ft^2$$

$$768$$ $$ft^2$$

Solution

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