Question

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Find the volume for each individual shape


Find the composite volume of the original figure.

Answer 1

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Explanation:

The combined shape consists of two hemispheres with radius of 2 mm and a circular cylinder with base radius of 2 mm and height of 10 mm.

Find the volume for each individual shape:

`V_(hemisphere)=(1)/(2)\cdot (4)/(3)\cdot \pi r^3=(2)/(3)\cdot \pi\cdot 2^3=(16)/(3)\pi \ mm^3`

`V_(cylinder)=\pi r^2h=\pi \cdot 2^2\cdot 10=40\pi \ mm^3`

Find the composite volume of the original figure:

`V{combined \ figure}=\\ \\=2V_(hemisphere)+V_(cylinder)=\\ \\=2\cdot (16)/(3)\pi +40\pi =\\ \\=(32)/(3)\pi +40\pi =\\ \\=(152)/(3)\pi \ mm^3`