Question

In a cone, 24 times of radius and 7 times of height are required to each other. If the volume of the cone is 3163 cm cube, find the measure of the slant height. ​

Answer 1

34.22cm

Explanation:

here,

24r = 7h

or, r = 7h/24

Volume of cone = 3163 cm cube

or, 1/3πr2h = 3163

or, 1/3 × 22/7 × (7h/24)2h = 3163

or, 22×49h2×h/3×7×576 = 3163

or, 1078h3 = 3163

or, h3 = 35491.32

hence, 32.86cm

then,

r = 7h/24

or, r = 7×32.86/24

hence, r = 9.58cm

now,

l2 = r2 + h2

or, l2 = (9.58)2 + (32.86)2

or, l2 = 91.77 + 1079.72

or, l2 = √1371.54

or, l = 34.22 cm

hence, the measure of the slant height is 34.22cm