Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 35

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Weekly Quiz Competition

Question 1
1 / -0

Find the surface area of a frustum of cone given below: (Use $$\pi$$ = 3)

A
3,992 cm$$^2$$

B
3,192 cm$$^2$$

C
2,192 cm$$^2$$

D
3,192 cm

Solution

Surface area of a frustum of cone = $$\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
D = 4 cm, d = 5 cm, s = 50 cm
Diameter = radius/2
Radius, R = 8 cm, r = 10 cm
$$= \pi(10 + 8)50 +\pi 10^2 + 8^2$$
$$= 3 \times (900 + 100 + 64)$$
$$= 3 \times (1,064)$$
$$= 3,192\, cm^2$$
Question 2
1 / -0

The frustum cone curved surface area is 2,489 $$m^2$$. The upper and lower circle area of a cone is 24 and 45 m. Find the total surface area.

A
2,558 $$m^3$$

B
2,558 m

C
2,398 $$m^3$$

D
2,408 $$m^3$$

Solution

Total surface area = $$\pi (R+r)s + A_1 + A_2 $$
Curved surface area = $$\pi (R + r)s \Rightarrow 2,489 m^2$$
$$A_1 = 45 m, A_2 = 24 m$$
Therefore, Total surface area $$= 2,489 + 45 + 24$$
TSA = 2,558 $$m^3$$
Question 3
1 / -0

The frustum cone curved surface area is 230 $$\pi cm^2$$. The upper and lower circle area of a cone is 12.5 and 16.5 cm. Find the total surface area. (Use $$\pi$$ = 3.14).

A
711.2 $$cm^3$$

B
721.2 $$cm^3$$

C
751.2 $$cm^3$$

D
731.2 $$cm^3$$

Solution

Total surface area = $$\pi (R+r)s + A_1 + A_2 $$
Curved surface area = $$\pi (R + r)s \Rightarrow 230 \pi m^2$$
$$A_1 = 12.5 cm, A_2 = 16.5 cm$$
Therefore, Total surface area =$$ 230 \times 3.14 + 12.5 +16.5$$
TSA = 751.2 $$cm^3$$
Question 4
1 / -0

The lateral area of the frustum of a right circular cone is equal to______________.

A
The difference of the circumference of the bases multiplied by slant height

B
The sum of the circumference of the bases multiplied by slant height

C
One-half the sum of the circumference of the bases multiplied by slant height

D
Two-third the sum of the circumference of the bases multiplied by slant height

Solution

The lateral area of the frustum of a right circular cone is equal to one-half the sum of the circumference of the bases multiplied by slant height.
Lateral area of the frustum cone $$= \dfrac{1}{2} (2\pi R + 2\pi r) l$$
Question 5
1 / -0

The lateral area of the frustum of a right circular cone is calculated by using the formula _________________.

A
$$\displaystyle \pi ( R + r) l$$

B
$$\displaystyle \pi ( R - r) l$$

C
$$\displaystyle \dfrac{\pi}{2} ( R + r) l$$

D
$$\displaystyle \dfrac{\pi}{2} ( R - r) l$$

Solution

The lateral area of the frustum of a right circular cone is equal to one-half of the sum of the circumferences of the bases multiplied by slant height.
Lateral area$$=\cfrac { 1 }{ 2 } \left( 2\pi R+2\pi r \right) l$$
$$=\left( \pi R+\pi r \right) l$$
$$=\pi\left( R+ r \right) l$$
Question 6
1 / -0

Find the surface area of a frustum of cone given below: (Use $$\pi$$ = 3.14)

A
2.0352 in$$^2$$

B
2.52 in$$^2$$

C
2.1352 in$$^2$$

D
2.1352 in

Solution

Surface area of a frustum of cone = $$\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
D = 0.2 in, d = 0.1 in, s = 0.8 in
Diameter = radius/2
Radius, R = 0.4 in, r = 0.2 in
= $$\pi$$(0.2 + 0.4)0.8 +$$\pi$$0.2$$^2$$ + $$\pi$$0.4$$^2$$
$$= 3.14 \times (0.48 + 0.04 + 0.16)$$
$$= 3.14 \times (0.68)$$
$$= 2.1352\, in^2$$
Question 7
1 / -0

Find the surface area of a frustum of cone given below: (Use $$\pi$$ = 3.14)

A
7,750 ft$$^2$$

B
7,650 ft$$^2$$

C
7,550 ft$$^2$$

D
7,850 ft$$^2$$

Solution

Surface area of a frustum of cone = $$\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
D = 10 ft, d = 5 ft, s = 100 ft
Diameter = radius/2
Radius, R = 20 ft, r = 10 ft
= $$\pi$$(10 + 10)100 + $$\pi$$10$$^2$$ + $$\pi$$20$$^2$$
= 3.14 $$\times$$ (2,000 + 100 + 400)
= 3.14 $$\times$$ (2,500)
= 7,850 ft$$^2$$
Question 8
1 / -0

The surface area of a frustum cone is 11,000 cm2. The larger and smaller radius of the cone is 10 and 5 cm. find its slant height. (Use $$\pi$$ = 22/7)

A
215 cm

B
235 cm

C
245 cm

D
225 cm

Solution

Surface area of a frustum of cone $$=\pi$$(r + R)s + $$\pi$$r$$^2$$ + $$\pi$$R$$^2$$
R = 10cm, r = 5cm, SA = 11,000 cm2
11,000 $$=$$ 22/7 $$\times$$ (5 +10)s +$$\pi$$5$$^2$$ + $$\pi$$10$$^2$$
11,000 $$=$$ 22/7 $$\times$$ [15s +25 + 100]
11,000 $$=$$ 22/7 $$\times$$ [15s +125]
11,000 $$\times$$ 7/22$$=$$ 15s + 125
3,500 125$$=$$ 15s
3,375/15 $$=$$ s
S $$=$$ 225 cm
Therefore, the slant height is 225 cm.
Question 9
1 / -0

The circumference of lower and upper bases of the frustum cone is 250 and 120 cm. The slant height is 12 cm. Find the curved surface area.

A
2,120 $$cm^2$$

B
2,220 $$cm^2$$

C
2,320 $$cm^2$$

D
2,020 $$cm^2$$

Solution

Curved surface area of the frustum cone = $$\displaystyle \frac{1}{2} (2\pi R + 2\pi r) l$$
$$= \displaystyle \frac{1}{2} (250 + 120) \times 12$$
$$= 370 \times 6$$
$$= 2,220$$ $$cm^2$$
Question 10
1 / -0

Find the surface area of a frustum of cone, whose larger and smaller radius is 10 and 2 mm. The slant height of the cone is 15 mm.

A
274$$\pi$$ mm$$^2$$

B
264$$\pi$$ mm$$^2$$

C
284$$\pi$$ mm$$^2$$

D
254$$\pi$$ mm$$^2$$

Solution

Surface area of a frustum of cone = $$\pi$$$$(r + R)s + $$$$\pi$$$$r$$$$^2$$$$ + $$$$\pi$$$$R$$$$^2$$

$$R = 10 mm$$, $$r = 2 mm$$, $$s = 15 mm$$
$$SA = (2 + 10)*15 +2 + 10$$
$$= \pi(12)15 + 4\pi + 100\pi$$
$$= \pi(180 + 4 + 100)$$
$$= 284\pi$$ mm$$^2$$

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Surface Areas and Volumes Test - 35

Result

Surface Areas and Volumes Test - 35

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SHARING IS CARING

Question 1

3,992 cm$$^2$$

3,192 cm$$^2$$

2,192 cm$$^2$$

3,192 cm

Solution

Question 2

2,558 $$m^3$$

2,558 m

2,398 $$m^3$$

2,408 $$m^3$$

Solution

Question 3

711.2 $$cm^3$$

721.2 $$cm^3$$

751.2 $$cm^3$$

731.2 $$cm^3$$

Solution

Question 4

The difference of the circumference of the bases multiplied by slant height

The sum of the circumference of the bases multiplied by slant height

One-half the sum of the circumference of the bases multiplied by slant height

Two-third the sum of the circumference of the bases multiplied by slant height

Solution

Question 5

$$\displaystyle \pi ( R + r) l$$

$$\displaystyle \pi ( R - r) l$$

$$\displaystyle \dfrac{\pi}{2} ( R + r) l$$

$$\displaystyle \dfrac{\pi}{2} ( R - r) l$$

Solution

Question 6

2.0352 in$$^2$$

2.52 in$$^2$$

2.1352 in$$^2$$

2.1352 in

Solution

Question 7

7,750 ft$$^2$$

7,650 ft$$^2$$

7,550 ft$$^2$$

7,850 ft$$^2$$

Solution

Question 8

215 cm

235 cm

245 cm

225 cm

Solution

Question 9

2,120 $$cm^2$$

2,220 $$cm^2$$

2,320 $$cm^2$$

2,020 $$cm^2$$

Solution

Question 10

274$$\pi$$ mm$$^2$$

264$$\pi$$ mm$$^2$$

284$$\pi$$ mm$$^2$$

254$$\pi$$ mm$$^2$$

Solution

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