Question

the volume of sphere is 36pie cubic cm find the surface area of the sphere​

Answer 1

Answer:

r = 3 cm

Step-by-step explanation:

The volume of the given sphere is #36pi cm^3#

The volume of every sphere is: #V=4pi*r^3/3#

So we can equate the two volumes:

#4pi*r^3/3 = 36pi cm^3#

Multiply both sides by #3#:

#4pi*r^3 = 108pi cm^3#

and divide both by #4pi#:

#r^3 = 27 cm^3#

#r = 3 cm#

Answer 2

$\bigstar \mid$ GIVEN :

• The volume of a sphere is $\sf 36\pi cm^3$

$\bigstar \mid$ TO FIND :

• The surface area of the sphere.

$\bigstar \mid$ SOLUTION :

We know the formula of

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

Using this formula,

$\sf \to \: volume \: of \: the \: sphere = \frac{4}{3} \pi {r}^{3}$

$\sf \to \: 36\pi = \frac{4}{3} \pi {r}^{3}$

$\sf \to \: \frac{ \cancel{36\pi } \times 3 }{ \cancel{4\pi}} = {r}^{3}$

$\sf \to \: 9 \times 3 = {r}^{3}$

$\sf \to \: {r}^{3} = 27$

$\sf \to \: r = \sqrt[3]{27}$

$\bf \to \: r \: = 9cm.$

Now,

Again, Using the formula

Surface area of the sphere = $\sf 4\pi r^2$

Hence,

Surface area of the sphere = $\sf \: 4\pi {r}^{2}$

Surface area of the sphere$\sf \: =4 \times {3}^{2} \pi$

Surface area of the sphere $\sf = 4 \times 9\pi$

$\sf \therefore$ Surface area of the sphere $\bf \: = 36\pi cm^2 ans.$