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
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Correct Answer: $468\pi$ cm3
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 $468\pi$ cm3.
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Question : The radius of a right circular cylinder is thrice of its height. If the height of the cylinder is 3.5 cm, what is the volume of the cylinder?
Option 1: 1124.25 cm3
Option 2: 1324.75 cm3
Option 3: 1468.25 cm3
Option 4: 1212.75 cm3
Question : What is the height of a cylinder whose radius of base is 12 cm and volume is 19008 cm3? [Use $\pi=\frac{22}{7}$]
Option 1: 6 cm
Option 2: 24 cm
Option 3: 38 cm
Option 4: 42 cm
Question : The radius of a cylinder is 14 cm. If the height of the cylinder is four times of its radius, then what is the curved surface area of the cylinder?
Option 1: 5546 cm2
Option 2: 4928 cm2
Option 3: 4694 cm2
Option 4: 5214 cm2
Question : The radius of a hemisphere is 5 cm. Find the volume.
Option 1: 330.4 cm3
Option 2: 117.9 cm3
Option 3: 150.6 cm3
Option 4: 261.9 cm3
Question : The radius of a right circular cylinder is 7 cm. Its height is thrice its radius. What is the curved surface area of the cylinder?
Option 1: 724 cm2
Option 2: 666 cm2
Option 3: 924 cm2
Option 4: 264 cm2
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