# ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.2 in Chapter 17 - Mensuration

Question 23 Mensuration Exercise 17.2

The volume of a right circular cone is 9856 cm3  and the area of its base is 616 cm2 .

Find the slant height of the cone.

Solution:

Assume that a cone has a height of "h" and a circular base with radius "r." This cone will have a volume that is one-third of the product of the base's area and its height.

Given base area of the cone = 616 cm2

π r2 = 616

(22/7)×r2 = 616

r2 = 616×7/22

r2 = 196

r = 14

Given volume of the cone = 9856 cm3

(1/3)π r2h = 9856

(1/3)×(22/7)×142 ×h = 9856

h = (9856×3×7)/(22×142)

h = (9856×3×7)/(22×196)

h = 48

Slant height, l = √(h2+r2)

l = √(482+142)

l = √(2304+196)

l = √(2500

l = 50

Hence the slant height of the cone is 50 cm.

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