Question 33

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Jambmaths question: 

A bucket is 12cm in diameter at the top, 8cm in diameter at the bottom and 4cm deep. Calculate its volume.

Option A: 

$\tfrac{304}{3}\pi c{{m}^{3}}$

Option B: 

$144\pi c{{m}^{3}}$

Option C: 

$\tfrac{128}{3}\pi c{{m}^{3}}$

Option D: 

$72\pi c{{m}^{3}}$

Jamb Maths Solution: 

$\begin{align}  & \text{Using similar triangles} \\ & \frac{4}{x}=\frac{6}{4+x} \\ & 4(4+x)=6x \\ & 16+4x=6x \\ & 2x=16 \\ & x=8 \\ & \text{The height of the cone formed be extension is}\left( 4+8 \right)cm=12cm \\ & \text{Volume of cone}=\tfrac{1}{3}\pi {{r}^{2}}h \\ & \text{Vol}\text{. of the bigger cone}=\tfrac{1}{3}\pi \times {{6}^{2}}\times 12c{{m}^{3}}=144\pi c{{m}^{3}} \\ & \text{Vol}\text{. of the smaller cone }=\tfrac{1}{3}\pi \times {{4}^{2}}\times 8c{{m}^{3}}=\frac{128}{3}\pi c{{m}^{2}} \\ & \text{Vol}\text{. of the bucket (or frustum)}=\left( 144\pi -\frac{128\pi }{3} \right)c{{m}^{3}} \\ & {{V}_{bucket}}=\frac{304\pi }{3}c{{m}^{3}} \\\end{align}$

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