This set of Aptitude Questions and Answers (MCQs) focuses on “Spheres and Hemispheres – Set 2”.

1. A sphere has a surface area of 425 cm^{2}. What will be the diameter of this sphere?

a) 29.478 cm

b) 37.826 cm

c) 33.806 cm

d) 27.647 cm

View Answer

Explanation: Given,

Volume = 425 cm

^{2}

Let the radius of the sphere = r

Volume = 4 / 3 πr

^{3}

➩ 425 = 4 / 3 * (22 / 7) * r

^{3}

➩ 425 * 3 * 7 / (22 * 4) = r

^{3}

➩ 101.42 = r

^{3}

➩ 33.806 = r

2. A hemispherical bowl is made of steel, 1 cm thick. The inner radius of the bowl is 4 cm. What will be the outer curved surface area (in sq. cm) of this bowl?

a) 157.14

b) 167.15

c) 148.34

d) 178.92

View Answer

Explanation: Given,

Inner radius = 4 cm

According to the question,

Outer radius = 5 cm

Curved surface area = 2 πr

^{2}

= 2 * (22 / 7) * (5)

^{2}

= 157.14 cm

^{2}

3. What will be the total surface area (in sq. cm) of a hemispherical bowl of radius 12 cm?

a) 1456.82

b) 1357.71

c) 1675.42

d) 1543.75

View Answer

Explanation: Given,

r = 12 cm.

Total surface area = 3 πr

^{2}

= 3 * (22 / 7) * (12)

^{2}

= 3 * (22 / 7) * 144

= 1357.71 cm

^{2}

4. If the radius of a sphere is tripled, then what will be the ratio of the surface area of original sphere to that of the new sphere?

a) 1:9

b) 1:3

c) 9:1

d) 3:1

View Answer

Explanation: Let the original radius = r

Original surface area = 4 πr

^{2}

According to the question,

New radius = 3r

New surface area = 4 π (3r)

^{2}

= 36 πr

^{2}

Ratio = original surface area / new surface area

= 4 πr

^{2}/ 36 πr

^{2}

= 1:9

5. A hemispherical bowl has total surface area 99 cm^{2}. What will be the curved surface area (in sq. cm) of five such bowls?

a) 342

b) 320

c) 330

d) 338

View Answer

Explanation: Given,

Total surface area = 99 cm

^{2}

Let the radius = r cm

Total surface area = 3 πr

^{2}

➩ 99 = 3 πr

^{2}

➩ 33 = (22 / 7) * r

^{2}

➩ 33 * 7 / 22 = r

^{2}

➩ r = 3.24 cm

Curved surface area of 5 such bowls = 5 * 2 πr

^{2}

= 10 * (22 / 7) * (3.24)

^{2}

= 330 cm

^{2}

6. What is the total surface area (in sq. cm) of a hemisphere whose curved surface area is 536 cm^{2}?

a) 887

b) 846

c) 925

d) 804

View Answer

Explanation: Given,

Curved surface area = 536 cm

^{2}

Let the radius = r

Curved surface area / total surface area = 2 πr

^{2}/ 3 πr

^{2}

➩ 536 / total surface area = 2 / 3

➩ 536 * 3 / 2 = total surface area

➩ Total surface area = 804 cm

^{2}.

7. What would be the surface area of a sphere of radius 14 cm?

a) 2464 cm^{2}

b) 3500 cm^{2}

c) 2756 cm^{2}

d) 3340 cm^{2}

View Answer

Explanation: Given,

Radius = 14 cm

Surface area = 4 πr

^{2}

= 4 * (22 / 7) (14)

^{2}

= 2464 cm

^{2}

8. The radius of first sphere is 6 cm and the radius of second sphere is 12 cm, then what will be the ratio of their curved surface area?

a) 1:3

b) 1:6

c) 1:4

d) 1:8

View Answer

Explanation: Given,

r

_{1}= 6 cm, r

_{2}= 12 cm

Ratio = curved surface area of first sphere / curved surface area of second sphere

= 4 πr

_{1}

^{2}/ 4 πr

_{2}

^{2}

= r

_{1}

^{2}/ r

_{2}

^{2}

= 36 / 144

= \(\frac {1}{4}\) or 1:4

9. What would be the total surface area of a hemisphere of diameter 14 cm?

a) 462 cm^{2}

b) 426 cm^{2}

c) 402 cm^{2}

d) 492 cm^{2}

View Answer

Explanation: Given,

Diameter = 14 cm

r = 7 cm

Total surface area of a hemisphere = 3 πr

^{2}

= 3 * (22 / 7) * (7)

^{2}

= 462 cm

^{2}

10. What will be the volume of a hemispherical bowl of radius 8 cm if it is three – fourth filled?

a) 256 π cm^{3}

b) 236 π cm^{3}

c) 286 π cm^{3}

d) 157 π cm^{3}

View Answer

Explanation: Given,

r = 8 cm

Volume of hemisphere thee – fourth filled = (3 / 4) * (2 / 3 πr

^{3})

= 3 / 4 * 2 / 3 * π * (8)

^{3}

= 256 π cm

^{3}

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