Question

半径为2的球内切于圆台,此圆台的母线与底面夹角为45°,求圆台的侧面积与体积

Answer 1

沿着轴心线做切面图,由等腰三角形性质、勾股定理、切线长定理得

4+r+2=4√2+√2 r

r=2√2-2

S侧=1/2*2π(4+r)*√2(4+r)-1/2*2πr*√2r

=32(√2-1)π

V=1/3*(4+2√2-2)^3-1/3*π*(2√2-2)^3

=2π/3*2*7

=28π/3