Geometry

Solids

Hard

From a solid cylinder whose height is 2.4 cm and diameter is 1.4 cm, a conical cavity of same height and same diameter is carved out. The total surface area of the remaining solid is:

Use $\pi = \frac{22}{7}$

18 cm $^2$

17.6 cm $^2$

17 cm $^2$

16.7 cm $^2$

✅ Correct Option: 2

$r = 0.7$ , $h = 2.4$ . Slant height $l = \sqrt{h^2 + r^2} = \sqrt{5.76 + 0.49} = \sqrt{6.25} = 2.5$ .

TSA of remaining solid = $2\pi r h + \pi r l + \pi r^2 = \pi r (2h + l + r)$ .

$= (22/7)(0.7)(4.8 + 2.5 + 0.7) = 2.2 \times 8 = 17.6$ cm $^2$ .

2022: 6 Oct Shift 1

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2025: 15 May Shift 1

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Choose the correct answer from the options given below:

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I. If the height of a cylinder is doubled, the area of the curved surface is doubled.

II. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold.

Which of the above statement(s) is / are true:

2022: 6 Oct Shift 1

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From a solid cylinder whose height is 2.4 cm and diameter is 1.4 cm, a conical cavity of same height and same diameter is carved out. The total surface area of the remaining solid is: Use π=227\pi = \frac{22}{7}π=722​