Question

Answered

From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. Take =22/7

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Answer 1

$\large{\underline{\rm{\blue{\bf{Given:-}}}}}$

Height of the solid cylinder = 2.8 cm

Diameter of the solid cylinder = 4.2 cm

$\large{\underline{\rm{\blue{\bf{To \: Find:-}}}}}$

The total surface area of the remaining solid.

$\large{\underline{\rm{\blue{\bf{Analysis:-}}}}}$

The surface area of the remaining solid = Curved surface area of cylindrical part + Curved surface area of the conical part + Area of the cylindrical base

$\large{\underline{\rm{\blue{\bf{Solution:-}}}}}$

We know that,

• d = Diameter
• h = Height
• r = Radius
• l = Slang height

Given that,

Height of the conical cylinder (h) = 2.8 cm

Diameter of the cylindrical part (d) = 4.2 cm

Radius of the conical part (r) = $\sf \dfrac{Diameter}{2}$

Radius of the conical part (r) = $\sf \dfrac{4.2}{2}$

$\implies \sf 2.1 \: cm$

Slant height of the conical part (l) = $\sf \sqrt{r^{2}+h^{2}}$

Substituting their values, we get

$\implies \sf \sqrt{(2.1)^{2}+(2.8)^{2}} \: cm$

$\implies \sf \sqrt{4.41+7.84} \: cm$

$\implies \sf \sqrt{12.25}$

$\implies \sf 3.5 \: cm$

According to the analysis given, we get

$\implies \sf 2 \pi rh + \pi rl+ \pi r^{2}$

Substituting their values,

$\sf \bigg( 2 \times \dfrac{22}{7} \times 2.1 \times 2.8 \times \dfrac{22}{7} \times 2.1 \times 3.5 +\dfrac{22}{7} \times 2.1 \times 2.1 \bigg) \: cm^{2}$

Solving this,

$\implies \sf (36.96+23.1+13.86) \: cm^{2}$

$\implies \sf 73.92 \: cm^{2}$

Therefore, the total surface area of the remaining solid is 73.92 cm²