Question

From a solid cylinder of height 24 cm and diameter 14 cm, a conical cavity of the
same height and same diameter is hollowed out. Find the total surface area of the
remaining solid.

Answer 1

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Answer 2

So,Total surface area of remaining solid is $1760cm^{2}$

Step-by-step explanation:

Given;

Height of cylinder$(h)=24cm$ and diameter$(d)=14cm$

Radius$(r)=\frac{d}{2}=7cm$

From figure,

∴$cb(l)=\sqrt{h^{2} +r^{2} }$

⇒$l=\sqrt{24^{2}+7^{2} }$

∴$l=25$$cm$

∴Total surface area of remaining solid$=$Area of cylinder$+$ Area of cone$+$Area of base

⇒Total surface area of remaining solid$=2\pi r h+\pi rl+\pi r^{2}$

⇒Total surface area of remaining solid$=(2\pi \times7\times 24)+(\pi\times 7\times25)+(\pi7^{2})$

⇒Total surface area of remaining solid$=\frac{22\times7}{7}( (2 \times 24)+25+7)$

⇒Total surface area of remaining solid$=22(48+32)$

∴Total surface area of remaining solid$=1760cm^{2}$

∴Total surface area of remaining solid is $1760cm^{2}$