Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 36

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Weekly Quiz Competition

Question 1
1 / -0

The surface area of a frustum cone is 330 in2. The larger and smaller radius of the cone is 2.2 and 1in. Find its slant height. (Use $$\pi$$ = 3.14)

A
2.6 in

B
3.6 in

C
5.6 in

D
4.6 in

Solution

Surface area of a frustum of cone = $$\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
R = 2.2in, r = 1 in, SA = 330 in2
330 $$=$$ 3.14 $$\times$$ (1 + 2.2)s +$$\pi$$1$$^2$$ + $$\pi$$2.2$$^2$$
330 $$=$$ 3.14 $$\times$$ [3.2s +1 + 4.84]
330 $$=$$ 3.14 $$\times$$ [3.2s + 5.84]
330/3.14 $$=$$ 3.2s + 5.84
105.09/5.84 $$=$$ 3.2s
17.994/3.2 $$=$$ s
S $$=$$ 5.6 in
Therefore, the slant height is 5.6 in.
Question 2
1 / -0

The surface area of a frustum cone is 3,300 mm$$^2$$. The larger and smaller radius of the cone is 5 and 2 mm. find its slant height. (Use $$\pi$$ = 22/7)

A
135.85 mm

B
145.85 mm

C
155.85 mm

D
165.85 mm

Solution

Surface area of a frustum of cone $$=\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
R = 5mm, r = 2mm, SA = 3,300 mm2
3,300 $$=$$ 22/7 $$\times$$ (2 +5)s +$$\pi$$2$$^2$$ + $$\pi$$5$$^2$$
3,300 $$=$$22/7 $$\times$$ [7s +4 + 25]
3,300 $$=$$22/7 $$\times$$ [7s + 29]
3,300 $$\times$$ 7/22$$=$$7s + 29
1,050 29 $$=$$ 15s
1,021/7 $$=$$ s
S = 145.85 mm
Question 3
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Find the surface area of a frustum of cone, whose larger and smaller radius is 12 and 5 m. The slant height of the cone is 20 m.

A
519$$\pi$$ m$$^2$$

B
509$$\pi$$ m$$^2$$

C
529$$\pi$$ m$$^2$$

D
539$$\pi$$ m$$^2$$

Solution

Surface area of a frustum of cone = $$\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
R = 12m, r = 5m, s = 20m
SA = $$\pi$$(5 + 12)20 +$$\pi$$5$$^2$$ + $$\pi$$12$$^2$$
= $$\pi$$(17)20 + 25$$\pi$$ + 144$$\pi$$
= $$\pi$$(340 + 25 + 144)
= 509 $$\pi$$m$$^2$$
Question 4
1 / -0

The circumference of lower and upper bases of the frustum cone is 43 and 37 in. The slant height is 30 in. What is the curved surface area ?

A
700 $$in^2$$

B
800 $$in^2$$

C
1,200 $$in^2$$

D
200 $$in^2$$

Solution

Curved surface area of the frustum cone
= $$\displaystyle \frac{1}{2}(2\pi R+2\pi r)l$$
= $$\displaystyle \frac{1}{2} (43 + 37) \times 30$$
= $$80 \times 15$$
= 1,200 $$in^2$$
Question 5
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The circumference of lower and upper bases of the frustum cone is 3.5 and 1.5 ft. The slant height is 5 ft. What is the curved surface area ?

A
12.5 $$ft^2$$

B
72.5 $$ft^2$$

C
11.5 $$ft^2$$

D
10.5 $$ft^2$$

Solution

Curved surface area of the frustum cone
$$=\displaystyle \frac{1}{2}(2\pi R+2\pi r)l$$
= $$\displaystyle \frac{1}{2} (3.5 + 1.5) \times 5$$
= $$5 \times 2.5$$
= 12.5 $$ft^2$$
Question 6
1 / -0

The surface area of a frustum cone is 2,200 cm2. The larger and smaller radius of the cone is 20 and 10 cm. find its slant height. (Use $$\pi$$ = 22/7).

A
7.666 cm

B
6.666 cm

C
8.666 cm

D
9.666 cm

Solution

Surface area of a frustum of cone $$=\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
R = 20cm, r = 10cm, SA = 2,200 cm2
2,200 $$=$$ 22/7 $$\times$$ (10+ 20)s +$$\pi$$10$$^2$$ + $$\pi$$20$$^2$$
2,200 $$=$$ 22/7 $$\times$$ [30s +100 + 400]
2,200 $$=$$ 22/7 $$\times$$ [30s +500]
2,200 $$\times$$ 7/22$$=$$ 30s + 500
700 500 $$=$$ 30s
200/30 $$=$$ s
S $$=$$ 6.666 cm
Question 7
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The circumference of lower and upper bases of the frustum cone is $$150$$ and $$20\ cm$$. The slant height is $$4.5\ cm$$. Find the curved surface area.

A
$$362.5\ cm^2$$

B
$$372.5\ cm^2$$

C
$$392.5\ cm^2$$

D
$$382.5\ cm^2$$

Solution

Curved surface area of the frustum cone $$=\displaystyle \frac{1}{2} (2\pi R + 2\pi r) l$$
$$=\displaystyle \frac{1}{2} (150 + 20) \times 4.5$$
$$=170 \times 2.25$$
$$= 382.5\ cm^2$$
Question 8
1 / -0

The circumference of lower and upper bases of the frustum cone is 13 and 27 mm. The slant height is 34 mm. What is the curved surface area ?

A
675 $$mm^2$$

B
680 $$mm^2$$

C
645 $$mm^2$$

D
650 $$mm^2$$

Solution

Curved surface area of the frustum cone
= $$\displaystyle \frac{1}{2}(2\pi R+2\pi r)l$$
= $$\displaystyle \frac{1}{2} (13 + 27) \times 34$$
= $$40 \times 17$$
= 680 $$mm^2$$
Question 9
1 / -0

The circumference of lower and upper bases of the frustum cone is 0.12 and 0.5 m. The slant height is 0.45 m. What is the curved surface area ?

A
0.4395 $$m^2$$

B
0.3395 $$m^2$$

C
0.2395 $$m^2$$

D
0.1395 $$m^2$$

Solution

Curved surface area of the frustum cone
= $$\displaystyle \frac{1}{2}(2\pi R+2\pi r)l$$
= $$\displaystyle \frac{1}{2} (0.12 + 0.5) \times 0.45$$
= $$0.62 \times 0.225$$
= 0.1395 $$m^2$$
Question 10
1 / -0

The circumference of lower and upper bases of the frustum cone is 10 and 20 cm. The slant height is 45 cm. What is the curved surface area ?

A
675 $$cm^2$$

B
600 $$cm^2$$

C
645 $$cm^2$$

D
450 $$cm^2$$

Solution

Curved surface area of the frustum cone
= $$\displaystyle \frac{1}{2}(2\pi R+2\pi r)l$$
= $$\displaystyle \frac{1}{2} (10 + 20) \times 45$$
= $$30 \times 22.5$$
= 675 $$cm^2$$

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Surface Areas and Volumes Test - 36

Result

Surface Areas and Volumes Test - 36

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SHARING IS CARING

Question 1

2.6 in

3.6 in

5.6 in

4.6 in

Solution

Question 2

135.85 mm

145.85 mm

155.85 mm

165.85 mm

Solution

Question 3

519$$\pi$$ m$$^2$$

509$$\pi$$ m$$^2$$

529$$\pi$$ m$$^2$$

539$$\pi$$ m$$^2$$

Solution

Question 4

700 $$in^2$$

800 $$in^2$$

1,200 $$in^2$$

200 $$in^2$$

Solution

Question 5

12.5 $$ft^2$$

72.5 $$ft^2$$

11.5 $$ft^2$$

10.5 $$ft^2$$

Solution

Question 6

7.666 cm

6.666 cm

8.666 cm

9.666 cm

Solution

Question 7

$$362.5\ cm^2$$

$$372.5\ cm^2$$

$$392.5\ cm^2$$

$$382.5\ cm^2$$

Solution

Question 8

675 $$mm^2$$

680 $$mm^2$$

645 $$mm^2$$

650 $$mm^2$$

Solution

Question 9

0.4395 $$m^2$$

0.3395 $$m^2$$

0.2395 $$m^2$$

0.1395 $$m^2$$

Solution

Question 10

675 $$cm^2$$

600 $$cm^2$$

645 $$cm^2$$

450 $$cm^2$$

Solution

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