Example 8

Transcript

Example 8 A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere. Given that, child reshapes cone with sphere. So, Volume of sphere = Volume of cone Volume of cone Height of cone = h = 24 cm Radius = r = 6 cm So, volume of cone = 1/3 πr2h = 1/3 π×(6)2×24 = 1/3 π×36×24 = 288π cm3 Volume of sphere Let radius of sphere = r Volume of sphere = 4/3 𝜋𝑟3 Now, Volume of sphere = volume of cone 4/3 𝜋𝑟3 = 288π 4/3 𝑟3 = 288 r3 = (288 × 3 )/4 r3 = 72 × 3 r3 = 8 × 9 × 3 r3 = (2 × 2 × 2 × 3 × 3 × 3) r = 〖"(2 " ×" 2 " ×" 2 " ×" 3 " ×" 3 " ×" 3)" 〗^(1/3) r = 〖"(2 " ×" 2 " ×" 2)" 〗^(1/3) × 〖"(3 " ×" 3 " ×" 3)" 〗^(1/3) r = 〖"(23)" 〗^(1/3) × 〖"(33)" 〗^(1/3) r = 2 × 3 r = 6 cm Hence , radius of sphere = 6 cm