Question : What is the area of the curved surface of a right circular cone with a height of 8 m and a slant height of 10 m?
Option 1: $60\mathrm{~m}^2$
Option 2: $60\pi \mathrm{~m}^2$
Option 3: $40 \mathrm{~m}^2$
Option 4: $ 40 \pi \mathrm{~m}^2$
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Correct Answer: $60\pi \mathrm{~m}^2$
Solution : Given: Height($h$) = 8 m and slant height($l$) = 10 m Radius($r$) = $\sqrt{l^2-h^2}$ = $\sqrt{10^2-8^2}$ = $\sqrt{100-64}$ = $\sqrt{36}$ = 6 m Area of the curved surface of a right circular cone = $ \pi rl$ = $\pi×6×10$ = $60\pi $ Hence, the correct answer is $60\pi \mathrm{~m}^2$.
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Question : The lateral surface area of a frustum of a right circular cone, if the area of its base is 16$\pi$ cm2, the diameter of the circular upper surface is 4 cm and the slant height is 6 cm, will be:
Option 1: $30\pi$ cm2
Option 2: $48\pi$ cm2
Option 3: $36\pi$ cm2
Option 4: $60\pi$ cm2
Question : The curved surface area of a right circular cone of a base radius of 21 cm is 594 sq. cm. What is the slant height of the cone?
Option 1: 15 cm
Option 2: 11 cm
Option 3: 9 cm
Option 4: 6 cm
Question : The volume of a solid right circular cylinder of height 8 cm is $392 \pi$ cm3. Its curved surface area (in cm2) is:
Option 1: $161 \pi$
Option 2: $96 \pi$
Option 3: $210 \pi$
Option 4: $112 \pi$
Question : The radius of a solid right circular cone is 36 cm and its height is 105 cm. The total surface area (in cm2) of the cone is:
Option 1: $4296 \pi$
Option 2: $3996 \pi$
Option 3: $5292 \pi$
Option 4: $3969 \pi$
Question : The circumference of the base of a right circular cone is 44 cm and its height is 24 cm. The curved surface area (in cm2) of the cone is: (Take $\pi=\frac{22}{7}$)
Option 1: 528
Option 2: 572
Option 3: 550
Option 4: 440
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