The radius and height of a cone are in the ratio 3:4.The area of the base of the cone is 113.04 cm square. Find the radius, height and curved surface area of the cone. (use piy3.14)
Answers
Given:
The radius and height of a cone are in the ratio 3:4.The area of the base of the cone is 113.04 cm square.
To find:
Find the radius, height and curved surface area of the cone.
Solution:
From given, we have the data as follows.
The radius and height of a cone are in the ratio 3:4.
Let, the radius of the cone be, 3x
The height of the cone be, 4x
The area of the base of the cone, A = πr²
113.04 = 3.14 × (3x)²
113.04/3.14 = 9x²
upon solving the above equation, we get,
x = 2, -2
Therefore, the values of radius and the height are:
The radius, r = 3x
r = 3(2)
r = 6 cm.
The height, h = 4x
h = 4(2)
h = 8 cm.
The curved surface area of the cone is,
S = πrl
S = πr √[r² + h²]
S = 3.14 × 6 √[6² + 8²]
S = 18.84 [10]
S = 188.4 cm²
The radius, height and the curved surface area of the cone are 6 cm, 8 cm and 188.4 cm²