This set of Aptitude Questions and Answers (MCQs) focuses on “Cone”.
1. Which of the following is the correct option related to the volume of a cone?
a) 1 / 4 πr2h
b) 1 / 6 πr2h
c) 1 / 3 πr2h
d) 1 / 12 πr2h
View Answer
Explanation: Let the radius = r, height = h.
The volume of a cone = 1 / 3 πr2h.
2. What will be the volume (in cubic cm) of a cone if its radius is 3 cm and height is 7 cm?
a) 66
b) 44
c) 88
d) 22
View Answer
Explanation: Given,
r = 3 cm, h = 7 cm
Volume of cone = 1 / 3 πr2h
= 1 / 3 * (22 / 7) * (3)2 * 7
= 66 cm3
3. What will be the volume (in cubic cm) of a conical vessel if its base area is 300 cm2 and its height is 90 cm?
a) 6000
b) 9000
c) 3000
d) 1000
View Answer
Explanation: Given,
Base area = 300 cm2, h = 90 cm
Volume of cone = (1 / 3) * base area * h
= (1 / 3) * 300 * 90
= 9000 cm3
4. What will be the radius of a circular cone of height 7 cm and volume 81 cm3?
a) 3.32 cm
b) 3.99 cm
c) 2.67 cm
d) 4.09 cm
View Answer
Explanation: Given,
h = 7 cm, Volume = 81 cm3
Volume of cone = 1 / 3 πr2h
➩ 81 = 1 / 3 (22 / 7) r2(7)
➩ 11.04 = r2
➩ r = 3.32 cm
5. Which of the following is the correct expression for the curved surface area of a cone?
a) 4πrl
b) (1 / 2) πrl
c) πrl
d) 2πrl
View Answer
Explanation: Let the radius = r and height = l.
Curved surface area of a cone = πrl.
6. Which of the following is the correct expression for the total surface area of a cone?
a) 4πr (r + l)
b) 2πr (r + l)
c) (1 / 2) πr (r + l)
d) πr (r + l)
View Answer
Explanation: Let the radius = r and height = l.
Total surface area of a cone = πr (r + l).
7. What will be the volume of a right circular cone of radius z cm and height 3z cm?
a) πz3
b) 3πz3
c) 9πz3
d) (1 / 3) πz3
View Answer
Explanation: Given,
R = z, l = 3z
Volume of cone = (1 / 3) πr2l
= (1 / 3) π * (z)2 * (3z)
= πz3
8. Two similar cones have equal curved surface area with radii in the ratio 1:4. What will be the ration of their heights?
a) 1:2
b) 2:1
c) 4:1
d) 1:4
View Answer
Explanation: Let the radius of first cone = r, height = h1
According to the question,
Radius of second cone = 4r and let the height = h2.
As the curved surface area are equal,
πrh1 = π(4r) * h2
h1 / h2 = 4 / 1
h1:h2 = 4:1
9. Two similar cones have equal volume with the ratio of their radii as 1:2. What will be the ratio of their heights?
a) 1:4
b) 4:1
c) 1:2
d) 2:1
View Answer
Explanation: Let the radius of first cone = r, height = h1
According to the question,
Radius of second cone = 2r and let the height = h2.
As the volume are equal,
1 / 3 πr2h1 = 1 / 3 π(2r)2h2
➩ h1 / h2 = 4 / 1
➩ h1:h2 = 4:1
10. What will be the diameter (in cm) of a right circular cone of height 8 cm and volume 95 cm3?
a) 9.52
b) 14.46
c) 8.93
d) 12.48
View Answer
Explanation: Given,
Volume = 95, h = 8
Let the radius = r
Volume = 1 / 3 πr2h
➩ 95 = 1 / 3 * (22 / 7) * r2 * 8
➩ (95 * 3 * 7) / 22 = r2
➩ 90.68 = r2
➩ 9.52 cm = r
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