The ratio of the radius of base to the height of a cylinder is 2:3. If the volume of the cylinder is 1617\text{ cm}^3, then what is the curved surface area of the cylinder? (Take \pi=\frac{22}{7})

Explanation

Let radius r = 2x and height h = 3x. Volume = \pi(2x)^2(3x) = 12\pi x^3 = 1617. Thus, 12 \times \frac{22}{7} \times x^3 = 1617 \implies x^3 = \frac{1617 \times 7}{264} = \frac{343}{8} \implies x = 1.5. Then r = 7, h = 10.5. Curved surface area = 2\pi rh = 2 \times \frac{22}{7} \times 7 \times 10.5 = 462\text{ cm}^2.

Related questions on Mensuration

• A pendulum swings through an angle of 30° and its end describes an arc of length 55 cm. What is the length of the pendulum? (Take $\pi = 22/...
• A conical tent has an angle of 60° at the vertex. If the curved surface area is 100 m^2, then what is the volume of the tent?
• A right circular cone and a hemisphere have equal base and equal volume. What is the ratio of the height of the cone to the radius of the he...
• A wire is in the form of an equilateral triangle with an area of 36\sqrt{3} cm^2. If it is changed into a semicircle, then what is its r...
• Let the area of the largest possible square inscribed in a circle of unit radius be x. Let the area of the largest possible circle inscribed...