# Mensuration-48

### From Homeworkwiki

**A cone of height 24 cm has a curved surface area 550 cm ^{2}. Find its volume.**

**Solution:** Let the radius be r cm and slant height l cm. Then

l^{2} = r^{2} + 24^{2}

=> l = √(r^{2} + 576)

It is given that curved surface = 550 cm^{2}

=> Π r l = 550

=> 22/7 x r x √(r^{2} + 576) = 550

=> r √(r^{2} + 576) = 25 x 7

=> r^{2} (r^{2} + 576) = (25 x 7)^{2}

=> r^{4} + 576 r^{2} - (625 x 49) = 0

=> r^{4} + 625 r^{2} - 49 r^{2} - 625 x 49 = 0

=> r^{2} (r^{2} + 625) - 49 (r^{2} + 625) = 0

=> (r^{2} + 625) (r^{2} - 49) = 0

=> r^{2} - 49 = 0

=> r = 7 (since r^{2} + 625 is not equal to zero)

Therefore, Volume = 1/3 x Π r^{2} h = 1/3 x 22/7 x 7 x 7 x 24 cm^{3} = **1232 cm ^{3}**