Question 34

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Jambmaths question: 

In the diagram above, a cylinder is surmounted by a hemispherical bowl. Calculate the volume of the solid.

Option A: 

180πcm3

Option B: 

162πcm3

Option C: 

216πcm3

Option D: 

198 πcm3

Jamb Maths Solution: 

$\begin{align}  & \text{Volume of cylinder }=\pi {{r}^{2}}h \\ & {{V}_{cylinder}}=\pi \times {{3}^{2}}\times 20=180\pi c{{m}^{3}} \\ & \text{Volume of hemisphere }=\tfrac{2}{3}\pi {{r}^{3}} \\ & {{V}_{hemisphere}}=\tfrac{2}{3}\times \pi \times {{3}^{3}}=18\pi c{{m}^{3}} \\ & \text{Volume of the composite}=(180\pi +18\pi )c{{m}^{3}} \\ & V=198\pi c{{m}^{3}} \\\end{align}$

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