Question

the volume of a right circular cylinder is 448πcm^2 and height is 7cm.find the lateral surface area and total surface area​

Answer 1

Answer:

Given:-

The volume of a cylinder =448$\pi cm^3$

Height=h=7cm

To find:-

Lateral surface area=Lsa

Total surface area =Tsa

Solution:-

Let radius =r

We know that in a Cylinder

$\boxed{\sf Volume=\pi r^2 h}$

$\qquad\quad\displaystyle\sf {:}\longrightarrow \pi r^2(7)=448\pi$

$\qquad\quad\displaystyle\sf {:}\longrightarrow 7r^2=448$

$\qquad\quad\displaystyle\sf {:}\longrightarrow r^2=\dfrac {448}{7}$

$\qquad\quad\displaystyle\sf {:}\longrightarrow r^2=64$

$\qquad\quad\displaystyle\sf {:}\longrightarrow r=\sqrt {64}$

$\qquad\quad\displaystyle\sf {:}\longrightarrow r=8cm$

• Radius =8cm

$\boxed{\sf LSA=2\pi rh}$

$\qquad\quad\displaystyle\sf {:}\longrightarrow LSA=2\dfrac {22}{7}×8×7$

$\qquad\quad\displaystyle\sf {:}\longrightarrow LSA=\dfrac {44}{56}{7}$

$\qquad\quad\displaystyle\sf {:}\longrightarrow LSA=44×8$

$\qquad\quad\displaystyle\sf {:}\longrightarrow LSA=352cm^2$

$\boxed{\sf TSA=2\pi r (h+r)}$

$\qquad\quad\displaystyle\sf {:}\longrightarrow TSA=2×\dfrac {22}{7}×8 (8+7)$

$\qquad\quad\displaystyle\sf {:}\longrightarrow TSA=\dfrac {44×8}{7}(15)$

$\qquad\quad\displaystyle\sf {:}\longrightarrow TSA=\dfrac {352×15}{7}$

$\qquad\quad\displaystyle\sf {:}\longrightarrow TSA=\dfrac {5280}{7}$

$\qquad\quad\displaystyle\sf {:}\longrightarrow TSA=754.2 cm^2$

Answer 2

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