Question

The curved surface area of a right circular cylinder is twice the sum of areas of its two circular faces. Find the ratio of the height and radius of the cylinder ​

Answer 1

Given :-

• The curved surface area of a right circular cylinder is twice the sum of areas of its two circular faces.

To Find :-

• The ratio of the height and radius of the cylinder.

Answer :-

• The ratio of the height and radius of the cylinder is 2:1

Explaination :-

Let Height be 'h' and radius be 'r'.

★ According to Question now

→ Curved Surface Area of Cylinder = 2(Sum of area of two circular faces)

→ 2πrh = 2(πr² + πr²)

→ 2πrh = 2(2πr²)

Substracting 2πr from both the sides we get :

→ h = 2r

→ h/r = 2/1

Therefore,the required ratio of the height and radius of the cylinder is 2:1.

Answer 2

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: Question :- \: \star}}}}}$

The curved surface area of a right circular cylinder is twice the sum of areas of its two circular faces. Find the ratio of the height and radius of the cylinder .

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

$\therefore\underline{\boxed{\textsf{Ratio = {\textbf{2 : 1}}}}} \qquad\qquad \bigg\lgroup\bold{Height \ and \ Radius \ Ratio} \bigg\rgroup$

$\Large{\underline{\underline{\bf{GiVen:-}}}}$

Curved Surface Area of Cylinder = 2(Sum of area of two circular Faces)

$\Large{\underline{\underline{\bf{Find:-}}}}$

Find the ratio of the height and radius of the cylinder .

$\Large{\underline{\underline{\bf{Solution:-}}}}$

As according to the given :-

So, we consider

Height be 'h'

radius be ' r'

From given :-

➹ 2πrh = 2(πr² + πr²)

➹2πrh = 2(2πr²)

Now ,

Both sides subtracting 2πr

★h = 2r

★ h/r = 2/1

$\therefore\underline{\boxed{\textsf{Ratio = {\textbf{2 : 1}}}}} \qquad\qquad \bigg\lgroup\bold{Height \ and \ Radius \ Ratio} \bigg\rgroup$

Some important formulas :-

Cylinder (surface of side) »»————> perimeter of circle × height

Cylinder (whole surface) »»————> Areas of top and bottom circles + Area of the side