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Volume and Surface Areas of Solids — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsVolume and Surface Areas of Solids5 Marks
Question
From a solid cylinder whose height is 8cm and radius 6cm, conical cavity of height 8cm and of base radius 6cm is hollowed out. Find the volume of the remaining solid. Also, find the total surface area of the remaining solid. [Taken $\pi$ = 3.14.]
✓

Answer

  1. Radius of cylinder = 6cm
Height of cylinder = 8cm



Volume of cylinder

$=\pi\text{r}^2\text{h}\text{ cu. units}$

$=\pi\times6\times6\times8\text{cm}^3$

$=288\pi\text{cm}^3$

Volume of cone removed

$=\frac{1}{3}\pi\text{r}^2\text{h}$

$=\frac{1}{3}\times\pi\times6\times6\times8\text{cm}^3$
  1. Surface area of cylinder $2\pi=2\pi\times6\times8\text{cm}^2=96\pi\text{cm}^2$
Slant height of cone $=\sqrt{6^2+8^2}=\sqrt{36+64}\text{cm}$

$=\sqrt{100}\text{cm}=10\text{cm}$

Curved surface area of remaining solid

$=(96\pi60\pi+36)\text{cm}^2$

$=192\pi\text{cm}^2=602.88\text{cm}^2$

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