Question : A toy is in the shape of a cylinder surmounted by a hemisphere. The total height of the toy is 15 cm and the radius of the hemisphere is 6 cm. What is the volume of the toy?
Option 1: $496\pi$ cm3
Option 2: $476\pi$ cm3
Option 3: $458\pi$ cm3
Option 4: $468\pi$ cm3
Correct Answer: $468\pi$ cm 3
Solution :
Given: Total height of the toy = 15 cm
The radius of the hemisphere (which is also the radius of the base of the cylinder) = 6 cm
Height of the cylinder = total height – radius of hemisphere
= 15 cm – 6 cm
= 9 cm
Now, the volume of the cylinder and the hemisphere:
Volume of the cylinder = $\pi \times (6)^2 \times 9 = 324\pi$
Volume of the hemisphere = $\frac{2}{3} \pi \times (6)^3 = 144\pi $
The total volume of the toy = $324\pi+144\pi$
= $468\pi$
Hence, the correct answer is $468\pi$ cm
3
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