Question

if the volume V of a cylinder, its curved A,and its radius of base is r then prove that 2V=Ar.

Answer 1

to prove- 2V=Ar
proof-
LHS
2V=2×πr²h
2V=2πrh(r)
2V=Ar
LHS=RHS
HENCE, PROVED

hope this answer will help you.

Answer 2

$2V = Ar$ ⇒ Hence Proved.

Step-by-step explanation:

Given:

V = Volume of Cylinder

A = Curved Surface area of Cylinder.

r = radius of the base

We need to prove that $2V=Ar$

Solution:

$2V=Ar$

First we will solve for L.H.S.

Volume of cylinder is given by π times square of radius r times height h.

Framing in equation form we get;

$V = \pi r^2h$

Multiplying 2 on both side we get;

$2V =2\pi r^2h$ ⇒ equation 1

Now Solving for R.H.S.

Curved surface Area of cylinder is given by 2 times π times radius r times height h.

Framing in equation form we get;

$A= 2\pi rh$

Multiplying both by 'r' we get;

$Ar=2 \pi r^2h$ ⇒ equation 2

from equation 1 and equation 2 we can see R.H.S of both sides are equal hence LHS will be equal too by Law of transitivity.

Hence LHS = RHS

$2V = Ar$ ⇒ Hence Proved.