Question : The height and the total surface area of a right circular cylinder are 4 cm and 8$\pi$ sq cm, respectively. The radius of the base of the cylinder is:
Option 1: $\left ( 2\sqrt{2}-2 \right )\ \text{cm}$
Option 2: $\left ( 2-\sqrt{2}\right )\ \text{cm}$
Option 3: $2\ \text{cm}$
Option 4: $\sqrt{2}\ \text{cm}$
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Correct Answer: $\left ( 2\sqrt{2}-2 \right )\ \text{cm}$
Solution : Given: Height of the cylinder = 4 cm Total surface area = 8$\pi$ cm2 ⇒ $2\pi r(h+r) = 8\pi$ ⇒ $r(4+r) = 4$ ⇒ $r^2+4r-4=0$ Using quadratic formula: $r= \frac{-b\pm \sqrt{b^2-4ac}}{2a}$ ⇒ $r= \frac{-4\pm \sqrt{4^2+4\times1\times4}}{2\times1}$ ⇒ $r= \frac{-4\pm \sqrt{16+16}}{2}$ ⇒ $r=\frac{-4\pm 4\sqrt{2}}{2}$ $\therefore r=(2\sqrt{2}-2)\ \text{cm}$ Hence, the correct answer is $(2\sqrt{2}-2)\ \text{cm}$.
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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 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 cylinder of height 56 cm is 1408 cm². Find the diameter of the base of the cylinder.
Option 1: 8 m
Option 2: 0.04 m
Option 3: 0.08 m
Option 4: 0.008 m
Question : A sphere has the same curved surface area as a cone, with a vertical height of 40 cm and a radius of 30 cm. The radius of the sphere is:
Option 1: $5 \sqrt 5 \text{ cm}$
Option 2: $5\sqrt 3\text{ cm}$
Option 3: $5\sqrt{15}\text{ cm}$
Option 4: $5\sqrt{10}\text{ cm}$
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
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