Question

a cylinder whose height is equal to it's diameter has the same volume as the sphere of radius 4 cm calculate the cube of radius to the base of the cylinder correct to one decimal place.​

Answer 1

Answer:

Answer. Volume of sphere=4/3πr. cube. =5632/21=44/7 r

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=2rh=d=2r

So, h = 2r

So, height = 2r

radius = r

Volume of cylinder = \pi r^{2} hπr

2

h

= \pi r^{2} 2(r)πr

2

2(r)

= 2\pi r^{3}2πr

3

Radius of sphere = 4 cm

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

3

4

πr

3

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

3

4

π(4)

3

= \frac{256}{3} \pi

3

256

π

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

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

3

256

π=2πr

3

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

6

256

=r

3

42.6666666667 =r^{3}42.6666666667=r

3

\sqrt[3]{42.6666666667} = r

3

42.6666666667

=r

3.49 = r3.49=r

Hence the radius of cylinder is 3.49 cm