This set of Aptitude Questions and Answers (MCQs) focuses on “Volume and Surface Area – Set 2”.
1. What will be the curved surface area of a hemisphere of radius r?
a) 6πr2
b) 2πr2
c) 3πr2
d) 4πr2
View Answer
Explanation: Given,
Radius = r
The correct formula for the curved surface area of a hemisphere = 2πr2.
2. What will be the total surface area of a closed hemisphere of radius r?
a) 6πr2
b) 2πr2
c) 3πr2
d) 4πr2
View Answer
Explanation: Given,
radius = r
Total surface area = curved surface area + base area
= 2πr2 + πr2
= 3 πr2
3. If the radius of a cylinder is halved and height is doubled, then how will its curved surface area change?
a) Halved
b) Equal
c) Doubled
d) Quadrupled
View Answer
Explanation: Let the original radius = r, height = h
Original curved surface area = 2πrh
According to the question,
New radius = r / 2, height = 2h
New curved surface area = 2π(r / 2) (2h)
= 2πrh
Hence both original curved surface area and new curved surface area are equal.
4. What will be the volume (in cubic cm) of cylindrical vessel having radius as 4 cm and height as 10 cm?
a) 160π
b) 180π
c) 140π
d) 120π
View Answer
Explanation: Given,
r = 4 cm, h = 10 cm
Volume = πr2h
= π * (4)2 * (10)
= 160π cm3
5. What is the total surface area (in sq. m) of a covered rectangular tank having dimensions as 4m * 5m * 6m?
a) 124
b) 74
c) 148
d) 98
View Answer
Explanation: Given,
l = 4m, b = 5m, h = 6m
Total surface area = 2(lb + bh + hl)
= 2 (4 * 5 + 5 * 6 + 6 * 4)
= 2 (20 + 30 + 24)
= 2 (74)
= 148 m2
6. If the radius of a sphere is tripled, then what will be the ratio of their surface area?
a) 3:1
b) 1:3
c) 9:1
d) 1:9
View Answer
Explanation: Let the radius of original sphere = r
Original surface area = 4πr2
According to the question,
New radius = 3r
New surface area = 4π(3r)2
= 36πr2
On comparing the ratio is 1:9.
7. If the edge length of a cube is reduced to one – third, then by how many times is the new surface area?
a) 1 / 9 times
b) 1 / 3 times
c) 1 / 12 times
d) 1 / 15 times
View Answer
Explanation: Let the original length = a
Original surface area = 6a2
According to the question,
New length = a / 3
New surface area = 6(a / 3)2
= 2a2 / 3
Thus, on comparing it comes out to be 1 / 9 times.
8. If the edge length of a cube is reduced by one – third time, then the ratio of old to new volume?
a) 8:27
b) 9:4
c) 27:8
d) 4:9
View Answer
Explanation: Let the original side length = s
Original volume = s3
According to the question,
New side length = 2s / 3
New volume = (2s / 3)3
= 8s3 / 27
Ratio = s3 / (8s3 / 27)
= 27:8
9. How is the volume of a cone affected if its radius is tripled?
a) 3 times
b) 9 times
c) 81 times
d) 27 times
View Answer
Explanation: Let original radius = r, height = h
Original volume = 1 / 3 πr2h
According to the question,
New radius = 3r, height = h
New volume = 1 / 3 π(3r)2h
On comparison new volume is 9 times the original.
10. What will be the volume of a cylindrical vessel having base area as 100 cm2 and height as 10 cm?
a) 1000 cm3
b) 900 cm3
c) 1100 cm3
d) 1200 cm3
View Answer
Explanation: Given,
Base area = 100 cm2, height = 10 cm
Volume = base area * height
= 100 * 10
= 1000 cm3
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