Question

a cylinder whose height is equal to its diameter has the same volume as a sphere of radius 4cm calculate the radius of the base of cylinder correct to one decimal place

Answer 1

Volume of sphere=4/3πr.cube.
=4/3×22/7×4×4×4
=
$5632 \div 21cm {}^{3}$
A/q. volume of sphere = volume of cylinder
Volume of cylinder=π r.sq. h
5632/21=π 2r cub.( as height is equal to diameter)
=5632/21=44/7 r.cub.
=42.6cm

Answer 2

Answer:

3.49 cm

Step-by-step explanation:

Let the Radius of cylinder be r

Since we are given that height of the cylinder is equal to diameter .

So, $h=d=2r$

So, h = 2r

So, height = 2r

radius = r

Volume of cylinder = $\pi r^{2} h$

                                = $\pi r^{2} 2(r)$

                                = $2\pi r^{3}$

Radius of sphere = 4 cm

Volume of sphere = $\frac{4}{3} \pi r^{3}$

                              = $\frac{4}{3} \pi (4)^{3}$

                              = $\frac{256}{3} \pi$

Now we are given that the volume of cylinder is equal to volume of sphere

So, $\frac{256}{3} \pi = 2\pi r^{3}$

$\frac{256}{6} =r^{3}$

$42.6666666667 =r^{3}$

$\sqrt[3]{42.6666666667}  = r$

$3.49 = r$

Hence the radius of cylinder is 3.49 cm