The diagonal d of the cube with the side a is
d2=a2+a2+a2=3a2
d=3a Given d=203 cm.
Then
a=3d=3203=20(cm) The radius r of the circle inscribed in the square with the side a is
r=2a Then we have the right circular cone inscribed in a cube with the side a
radius=r=2a, height=h=a Slant height L is
L=r2+h2=(2a)2+a2=25a3. Surface area of a cone = Base Area + Curved Surface Area of a cone
A=πr2+πrL
A=π((2a)2+2a(25a))=4πa2(1+5)
A=4π(20)2(1+5)=100π(1+5)(cm2)
≈1016.64(cm2) The surface area of the cone is 100π(1+5) cm2≈1016.64 cm2.
4. The volume of the cube is
Vcube=a3 The volume of the cone is
Vcone=31πr2h=31π(2a)2(a)=12πa3 The volume of the space between the cone and the cube is
Vspace=Vcube−Vcone
=a3−12πa3=12a3(12−π)
Vspace=12(20)3(12−π)=32000(12−π)(cm3)
≈5905.605(cm3) The volume of the space between the cone and the cube is
32000(12−π) cm3≈5905.605 cm3.
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