Answer to Question #91632 in Geometry for Rejoice

Question

True /false
1.A spehere has radius 3a units.Right circula cylinder has a height 4times its radius which is a units.The ratio of the volume of the cylinder to the sphere is 1:9
2.Consider a circle with diameter d units and a square with diagonal d units.If a fly crawls round the circle once and an ant crawls round the square once , the fly travels further.
3.Volume of a right circular cone with height 15cm is the same as the volume of a right circulat cylinder with height 5cm, if the both have the same radius

Answer 1

1.True.

V₁ is the volume of the sphere, V₂ is the volume of the cylinder.

V₁ = $\frac{4}{3} \pi R^3,$ R=3a, V₂= $\pi r^2 h$, r=a, h=4r=4a.

V₂/V₁=4/36=1/9.

2.True.

S is the length of the circle, L is the length of the square,

S=$\pi d$, L=4x, x=$\sqrt{d^2/2}$

S>L

3.True.

V₁ is the volume of the cone, V₂ is the volume of the Cylinder.

V₁=$1/3\pi R^2 H,$ V₂=$\pi R^2 h,$ H=15, h=5.

V₁=V₂