The radius and the height of a right circular cone are in the ratio of `5 : 12` and its volume is 2512 cu cm. Find the curved surface area and the total surface area of the cone. (Use `pi = 3.14`)

Explanation

Let radius = 5x cm and height = 12x cm. Then,
volume `= [(1)/(3) xx 3.14 xx (5x)^(2) xx (12x)] cm^(3) = (314x^(3)) cm^(3)`
`:. 314x^(3) = 2512 rArr x^(3) = ((2512)/(314)) = 8 rArr x = 2`
`:.` radius = 10 cm and height = 24 cm
`:.` slant height `= sqrt(r^(2) + h^(2)) = sqrt((10)^(2) + (24)^(2)) cm`
`= sqrt(676) cm = 26 cm`
So, area of the curved surface `= pir l`
`= (3.14 xx 10 xx 26) cm^(2)`
`816.4 cm^(2)`
Total surface area = (curved surface area + base area)
`= (816.4 + 3.14 xx 10 xx 10) cm^(2)`
`= (816.4 + 314) cm^(2) = 1130.4 cm^(2)`