Question

the height and the shant height of a cone are 21cm and 28cm respectively. find the volume of the cone

Answer 1

given
dimensions of the cone are
height = h= 21 cm
slant height = l= 28 cm
base radius = r cm

r= √l²-h²
=√28² - 21²
= √(28+21)(28-21)
=√49*7
= 7√7 cm
i) volume = (πr²h)/3

= (22*7√7*7√7*21)/(3*7)
=7546 cm³

Answer 2

height , h = 21 cm
slant height , l = 28 cm
l ² = h² + r ²
∴  r ² = l ² - h² 
r² = (28) ² - (21)²
r ² = 784 - 441
r ² = 343
r = √ 343
r = √ 7 × 7 × 7
∴ r = 7 √ 7 cm

Volume = 1/3 π r² h
             = 1/ 3 × 22 / 7 × 7√7 ×7√7 ×21
             = 22 × 7√7 ×7√7 
             = 22 × 343
             = 7546 cm ³

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