The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surfcae area of the balloom in the two cases is

Options

A. `1:4`
B. `1:3`
C. `2:3`
D. `2:1`

Answer

A

Explanation

Given, radius of a hemispherical balloom `r_(1) = 6 cm`
since, air is pumped into balloom. Them, radius of a hemispherical balloon, `r_(2) = 12 cm`
`therefore` Ratio of the surface areas of the balloom in two cases `= (3pir_(1)^(2))/(3pir_(2)^(2))`
`rArr " "(r_(1)^(2))/(r_(2)^(2)) = ((6)^(2))/((12)^(2)) = (36)/(144) = (1)/(4) = 1 :4`
Hence, ratio of the areas of the balloom in two casaes in 1 :4