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

The perimeter of the base of a cone is 44 cm and the slant height is 25 cm. Find the volume and the curved surface 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 perimeter of the base of a cone = 44 cm

2π r = 44

2×22/7×r = 44

r = 44×7/(2×22)

r = 7 cm

Slant height, l = 25

height, h = √(l2-r2)

h = √(252-72)

h = √(625-49)

h = √576

h = 24 cm

Volume of the cone, V = (1/3)π r2h

V = (1/3)×(22/7)×72×24

V = (22/7)×49×8

V = 22×7×8

V = 1232

Hence the volume of the cone is 1232 cm3.

Curved surface area of the cone = π rl

= (22/7)×7×25

= 22×25

= 550 cm2

Hence the curved surface area of the cone is 550 cm2. Related Questions

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