Question

A grain silo is composed of a cylinder and a hemisphere. the diameter is 4.4 meters. the height of its cylindrical portion is 6.2 meters. a half-sphere is stacked on top of a cylinder. they both share a circular base. the cylinder has a height of 6.2 meters and the sphere has a diameter of 4.4 meters. what is the approximate total volume of the silo? use 3.14 for π and round the answer to the nearest tenth of a cubic meter. 37.1 m3 71.9 m3 116.5 m3 130.8 m3

Answer 1

The total volume of the silo is 116.6 m³.

What is a grain silo in this problem?

It is a solid where a hemisphere is kept on top of a cylinder sharing common circular bases.

Diameter of the cylinder of the silo= 4.4m

So, the radius r of the cylinder will be = 2.2m

The radius r of hemisphere = 2.2m (same as cylinder due to common circular bases)

Height h of the cylinder = 6.2m

The total volume of the silo will be the combined volume of the cylinder and hemisphere.

The volume of cylinder = $\pi r^{2} h$

The volume of hemisphere = $\frac{2}{3} \pi r^{3}$

Total volume = $\pi r^{2} h+ \frac{2}{3} \pi r^{3}$

total volume = $\pi r^{2} (h+\frac{2}{3} r)$

Total volume = $\pi *2.2^{2} (6.2+\frac{2}{3} *2.2)$

Total volume = 116.6 m³.

Therefore, the total volume of the silo is 116.6 m³.

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