From a solid cylinder of height 2.4 cm and radius 0.7 cm, a conical cavity of the same height and same radius is…

CBSE Class 10 Maths PYQ · Surface Areas & Volumes · Both · 5 Marks · July 2025 · Standard

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615 Marks · July 2025 · Standard
From a solid cylinder of height $2.4$ cm and radius $0.7$ cm, a conical cavity of the same height and same radius is hollowed out. Find the volume and total surface area of the remaining solid.
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Volume of the remaining solid = Volume of cylinder - volume of cone
$= \pi \times (0.7)^2 \times 2.4 - \frac{1}{3} \times \pi \times (0.7)^2 \times 2.4$
$= 2.464 \text{ cm}^3$
Slant height of cone = $\sqrt{(0.7)^2 + (2.4)^2} = 2.5$ cm
Total Surface area = CSA of cylinder + CSA of cone + Area of base
$= 2 \times \frac{22}{7} \times 0.7 \times 2.4 + \frac{22}{7} \times 0.7 \times 2.5 + \frac{22}{7} \times (0.7)^2$
$= 17.6 \text{ cm}^2$
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