Question

The volume of a solid 2 points
cylinder is 448Tt cms and
it's height is 7cm find its
lateral surface area (ch
ठोस बेलन का आयतन 448T1
cm है व ऊँचाई 7cm है तो
उसका वक्र पृष्ठीय क्षेत्रफल ज्ञात​

Answer 1

For a solid cylinder -

Given :-

$\sf{Volume \: (V) = 448\pi \: cm^{3}}$

$\sf{height \: (h) = 7 \: cm}$

To Find :-

$\sf{Lateral \: Surface \: Area \: of \: this \: solid \: cylinder = ?}$

Using Formulas :-

$\sf{Volume \: of \: Solid \: Cylinder = \pi r^{2} h}$

$\sf{Lateral \: Surface \: Area = 2\pi r h}$

Solution :-

$\sf{Volume \: of \: Solid \: Cylinder = 448\pi}$

$\sf{\pi r^{2} h = 448\pi}$

$\sf{r^{2} h = 448}$

$\sf{r^{2}(7) = 448}$

$\sf{7r^{2} = 448}$

$\sf{r^{2} = 64}$

$\sf{r=\sqrt{64}}$

$\sf{r = 8 \: cm}$

Now ,

$\sf{Lateral \: Surface \: Area \: of \: Solid \: Cylinder -}$

$\sf{2\pi r h}$

$\sf{2\times \frac{22}{7}\times 8\times 7}$

$\sf{2\times 22\times 8}$

$\sf{2\times 176}$

$\sf{352 \: cm^{2}}$

Result :-

$\sf{Lateral \: Surface \: Area \: of \: this \: Solid \: Cylinder \: is \: 352 \: cm^{2}.}$