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The total surface area of a circular base cone is 9856 cm2 and the radius of the circular base of the cone is 28 cm. If the height of a cylinder is \(83\frac{1}{3}\% \) of the slant height of the cone and the radius of cylinder is 14 cm, then what is the volume of the cylinder?

The total surface area of a circular base cone is 9856 cm2 and the radius of the circular base of the cone is 28 cm. If the height of a cylinder is \(83\frac{1}{3}\% \) of the slant height of the cone and the radius of cylinder is 14 cm, then what is the volume of the cylinder? Correct Answer 43120 cm<sup>3</sup>

Given that,

Total surface area of the cone = 9856 cm2

The radius of circular base of the cone = 28 cm

Let the slant height of the cone = ‘l’ cm

According to the question∶

πr(l + r) = 9856

(22/7) × 28 × (l + 28) = 9856

l + 28 = 112

l = 84 cm

The height of the cylinder = 84 × (250/3) ×1/100 = 70 cm

The radius of the cylinder = 14 cm

Now, the volume of the cylinder = π × (14)2 × (70) = 43120 cm3

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