A right circular cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is
A. 3 : 5
B. 2 : 5
C. 3 : 1
D. 1 : 3
Answers
Given : A right circular cylinder and a right circular cone have the same radius and the same volume.
Let the base radius of the cylinder and the cone be 'r' and the volume of the cylinder and the cone be 'V' and the height of the cylinder and the cone be 'h1' and 'h2'.
Volume of cone = ⅓ πr²h
V/V = πr²h1/⅓ πr²h2
1 = h1/(⅓ × h2)
1 = h1 × 3/h2
1 = 3h1/h2
h2 = 3h1
h1/h2 = ⅓
h1 : h2 = 1 : 3
Hence, the ratio of the height of the cylinder to that of the cone is 1 : 3.
Option (D) 1 : 3 is correct.
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Let the base radius of the cylinder and the cone be 'r' and the volume of the cylinder and the cone be 'V' and the height of the cylinder and the cone be 'h1' and 'h2'.
Now,
Volume of cone = ⅓ πr²h
V/V = πr²h1/⅓ πr²h2
1 = h1/(⅓ × h2)
1 = h1 × 3/h2
1 = 3h1/h2
h2 = 3h1
h1/h2 = ⅓
h1 : h2 = 1 : 3