Question

Find the radius of base & height of a cylinder given that its volume is 770cm3 & area of its curved surface is 440 m².(plz explain step by step)​

Answer 1

Correct Question

Find the radius of base & height of a cylinder given that its volume is 770cm3 & area of its curved surface is 440 cm².

Solution

Given :-

• Volume of cylinder = 770 cm³
• Curved surface area of cylinder = 440 cm²

Find :-

• Radius and height of cylinder

Explanation

Let,

Radius of base of cylinder be" r ",height be " h "

Using Formula

★ Volume of cylinder = πr²h

★ Curved surface area = 2πrh

According to question

In Case (1).

==> Volume of cylinder = 770 cm³

==> πr²h = 770___________________(1)

Again,

==> Curved surface area of cylinder = 440 cm²

==> 2πrh = 440 _____________________(2)

Divide by equ(1) & equ(2)

==> πr²h/2πrh = 770/440

==> r/2 = 77/44

==> r = ( 77 × 2)/44

==> r = (7 × 2)/4

==> r = 7/2

Or,

==> r = 3.5 cm

For value of " Height "

keep value of " r " in equ(2)

==> 2π × 3.5 × h = 440

==> 7πh = 440

• π = 22/7

==> 7 × 22/7 × h = 440

==> 22h = 440

==> h = 440/22

==> h = 20 cm

Hence

• Radius of base of cylinder = 3.5 cm
• Height of cylinder = 20 cm

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Some Formula

★ Surface area of cylinder = 2πrh + πr²h

★Base area of cylinder = πr²

★ Diameter of cylinder = 2√(v/πh)

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