Question

A large sphere of radius 3.5 cm is carved from a cubical solid. Find the difference between their surface areas.​

Answer 1

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Answer 2

Answer:

The difference between their surface areas is 140 $cm^{2}$

Step-by-step explanation:

Given -

Radius of sphere - 3.5 cm

To find -

The difference between the surface areas of the cube and the sphere.

Solution -

We can follow the given approach to solve the question easily.

We have,

The radius of the sphere (r) =  3.5 cm

To calculate the surface area of the cubical solid we need to calculate its side.

Now, if the sphere has been carved from the cubical solid as stated in the question then clearly we can say that,

The side of the cubical solid (a) = The diameter of the sphere (d) = The radius × 2

The side of the cubical solid (a) = 3.5 × 2 = 7 cm

Hence, we have the side of the cubical solid as 7 cm.

We know that,

The surface area of sphere = 4π$r^{2}$

                                              = 4 × $\frac{22}{7}$ × 3.5 × 3.5

                                              = 154 $cm^{2}$

We have the surface area of the sphere as 154 $cm^{2}$

Now,

The surface area of cubical solid = 6$a^{2}$

                                                       = 6 × 7 × 7                      

                                                       = 294 $cm^{2}$

We have the surface area of the cubical solid as 294 $cm^{2}$

Then,

The difference between surface areas = 294 $cm^{2}$ - 154 $cm^{2}$

                                                                = 140 $cm^{2}$

Hence, the difference between the surface area of the sphere and the cubical solid is 140 $cm^{2}$