This set of Aptitude Questions and Answers (MCQs) focuses on “Spheres and Hemispheres – Set 2”.
1. A sphere has a surface area of 425 cm2. 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 cm2
Let the radius of the sphere = r
Volume = 4 / 3 πr3
➩ 425 = 4 / 3 * (22 / 7) * r3
➩ 425 * 3 * 7 / (22 * 4) = r3
➩ 101.42 = r3
➩ 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 πr2
= 2 * (22 / 7) * (5)2
= 157.14 cm2
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 πr2
= 3 * (22 / 7) * (12)2
= 3 * (22 / 7) * 144
= 1357.71 cm2
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 πr2
According to the question,
New radius = 3r
New surface area = 4 π (3r)2
= 36 πr2
Ratio = original surface area / new surface area
= 4 πr2 / 36 πr2
= 1:9
5. A hemispherical bowl has total surface area 99 cm2. 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 cm2
Let the radius = r cm
Total surface area = 3 πr2
➩ 99 = 3 πr2
➩ 33 = (22 / 7) * r2
➩ 33 * 7 / 22 = r2
➩ r = 3.24 cm
Curved surface area of 5 such bowls = 5 * 2 πr2
= 10 * (22 / 7) * (3.24)2
= 330 cm2
6. What is the total surface area (in sq. cm) of a hemisphere whose curved surface area is 536 cm2?
a) 887
b) 846
c) 925
d) 804
View Answer
Explanation: Given,
Curved surface area = 536 cm2
Let the radius = r
Curved surface area / total surface area = 2 πr2 / 3 πr2
➩ 536 / total surface area = 2 / 3
➩ 536 * 3 / 2 = total surface area
➩ Total surface area = 804 cm2.
7. What would be the surface area of a sphere of radius 14 cm?
a) 2464 cm2
b) 3500 cm2
c) 2756 cm2
d) 3340 cm2
View Answer
Explanation: Given,
Radius = 14 cm
Surface area = 4 πr2
= 4 * (22 / 7) (14)2
= 2464 cm2
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,
r1 = 6 cm, r2 = 12 cm
Ratio = curved surface area of first sphere / curved surface area of second sphere
= 4 πr12 / 4 πr22
= r12 / r22
= 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 cm2
b) 426 cm2
c) 402 cm2
d) 492 cm2
View Answer
Explanation: Given,
Diameter = 14 cm
r = 7 cm
Total surface area of a hemisphere = 3 πr2
= 3 * (22 / 7) * (7)2
= 462 cm2
10. What will be the volume of a hemispherical bowl of radius 8 cm if it is three – fourth filled?
a) 256 π cm3
b) 236 π cm3
c) 286 π cm3
d) 157 π cm3
View Answer
Explanation: Given,
r = 8 cm
Volume of hemisphere thee – fourth filled = (3 / 4) * (2 / 3 πr3)
= 3 / 4 * 2 / 3 * π * (8)3
= 256 π cm3
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