Question

Given the area of circular base and the area of curved surface of the cone are 98.56 cm² and 264 cm² respectively. Find the height of the cone, in cm.​

Answer 1

Answer: height = 13.9 cm

Step-by-step explanation:

The base area of a cone is the area of a circle. Given that base area = 98.56 cm^2

Base area = πr^2

Substitutes the value into the formula

98.56 = 22/7 × r^2

Cross multiply

689.92 = 22r^2

r^2 = 689.92/22

r = sqrt ( 31.36 )

r = 5.6 cm

Also, the curved surface area of a cone is πrL

Where the given value is 264 cm^2

Substitutes the value into the formula

264 = 22/7 × 5.6 × L

Where L = slant height

Cross multiply

123.2L = 1848

L = 1848 /123.2

L = 15 cm.

Using pythagorean theorem to find the height H of the cone.

H^2 = L^2 - r^2

H^2 = 15^2 - 5.6^2

H = sqrt( 193.64 )

H = 13.9 cm