# If the Volumes of Two Cones Are in the Ratio 1 : 4 and Their Diameters Are in the Ratio 4 : 5, Then Write the Ratio of Their Weights. - Mathematics

If the volumes of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, then write the ratio of their weights.

#### Solution

The ratio of the volume of cones

v_1 : v_2 = 1 : 4

And 2r_1 :2r_2 = 4 : 5,

i.e., r_1 / r_2 = 4/5

"Now", v_1/v_2 = (1/3 pir_1^2 h_1)/(1/3 pir_2^2 h_2)

1/4 = (r_1/r_2)^2 xx (h_1/h_2)

h_1/h_2 = 1/4 xx 25 /16

= 25/ 64

Hence, h_1 : h_2 = 25 : 64

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Q 8 | Page 87