Answer to Question #91632 in Geometry for Rejoice

Question #91632
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
1
Expert's answer
2019-07-17T11:32:34-0400

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

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