Question

What is the volume of the cylinder whose height is 4 times the radius

Answer 1

Answer:

h = 4r

r = h/4

volume = πr²h

             = π × h/4 × h/4 × h

             = πh³ / 8

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Answer 2

GIVEN

FOR A cylinder,

height is 4 times the radius

To find

Volume of the cylinder

Explanation

let radius of the cylinder =r units

then

height of the cylinder=4r

now we need to find the volume of cylinder

1)Interms of r:

$\underline{\sf volume \: of \: cylinder =\pi r^2h cubic \:units}$

$V=\pi r^2×4r$

$=>V=4\pi r^3$

$\boxed{\sf volume \:of \:the\: cylinder=4\pi r^3 \:cubic \:units}$

2)Interms of h:

$r=\dfrac{h}{4}$

Now

$V=\pi (\dfrac{h}{4})^2 h$

$V=\pi \dfrac{h^3}{16}$

$\boxed{\sf Volume\: of\: cylinder =\pi \dfrac{h^3}{16} cubic \: units }$

Extra information

For a cylinder,

$=>C.S.A=2\pi r$

$=> T.S.A=2\pi r(r+h)$