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A hollow cone is mounted below a hollow cylinder as shown in the figure. The height of the cylinder and the cone are equal to the radius of the base of the cylinder. If the lateral surface area this figure is 8π(4 + 2√2) cm2, what is the volume of the figure?

A hollow cone is mounted below a hollow cylinder as shown in the figure. The height of the cylinder and the cone are equal to the radius of the base of the cylinder. If the lateral surface area this figure is 8π(4 + 2√2) cm2, what is the volume of the figure? Correct Answer 268.2 cm<sup>3</sup>

Let the radius of the base of the cylinder be ‘r’ cm

∴ Height of the cylinder = Height of the cone = r cm

∴ Slant height of the cone = √(r2 + r2) = r√2 cm

∵ Lateral surface area of the figure = 8π(4 + 2√2)

⇒ π × r × r√2 + 2π × r × r = 8π(4 + 2√2)

⇒ πr2(2 + √2) = 16π(2 + √2)

⇒ r = 4

∴ Volume of the figure

= (1/3) × π × r2 × r + π × r2 × r

= (4/3) π × 43

= 256π/3 cm3

= 268.2 cm3

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