Question

from the top of a cone of a base of radius 24cm and height 45cm . a cone of slant height 17cm is cut off. what is the volume of the remaining frustum of the cone​

Answer 1

Answer:

First find solutions the first step to find slant height and then volume of frustum + volume of cone to get the answer solve it

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Answer 2

The volume of remaining frustum of the cone = 26148.6 cm³

r1 = radius of the original cone = 24 cm

r2 = radius of the cone cut off

l1 = slant height of the original cone = √(2601) = 61 cm

l2 = slant height of the cone cut off = 17 cm

h1 = height of the original cone = 45 cm

h2 = height of the cone cut off

For the cone and the frustum

=> l1/l2 = r1/r2

=> r2 = 24 × (17/61)

=> r2 = 8 cm

h2 = √((l2)² - (r2)²)

h2 = √225 = 15 cm

The volume of the original cone = π/3 × (r1)² h1

= (1/3) × (22/7) × (24)² × 45

= 27154.3 cm³

The volume of the cone cut off = π/3 × (r2)² h2

= (1/3) × (22/7) × (8)² × 15

= 1005.7 cm³

The volume of frustum = volume of original cone - volume of the cone cut off

= 27154.3 - 1005.7

= 26148.6 cm³