Question

圆柱与圆锥的体积比是9:10,圆柱底面直径与圆锥底面直径比是3:5,圆柱的高与圆锥的高比是?

Answer 1

设：圆柱体积V1,底面半径为R1,地面面积为S1,高为H1

圆锥体积V2,底面半径为R2,地面面积为S2,高为H2

V1=S1*H1=3.14*R1*R1*H1;

V2=1/3*S2*H2=1/3*3.14*R2*R2*H2;

所以：V1/V2=(3.14*R1*R1*H1)/(1/3*3.14*R2*R2*H2)=(3R1*R1/R2*R2)*(H1/H2);

H1/H2=(V1/V2)*(R2*R2/3*R1*R1);

由题意得：V1/V2=9/10;R1/R2=3/5

代入得：H1/H2=5/6