Question

From a metal made hemisphere of radius 2 cm, a maximum spherical part
is cut off. Find the price of the remaining part of metal if the price of 1
cc of metal is rs 7.​

Answer 1

Given:

From a metal made hemisphere of radius 2 cm, a maximum spherical part  is cut off.

To find:

The price of the remaining part of metal if the price of 1  cc of metal is Rs. 7

Solution:

Finding the volume of the hemisphere:

The radius of the metal hemisphere, r = 2 cm

∴ The volume of the metal hemisphere is,

= $\frac{2}{3} \pi r^3$

= $\frac{2}{3} \times \frac{22}{7} \times 2^3$

= $\bold{16.76\: cm^3}$

Finding the volume of the spherical part:

The maximum spherical part that is cut off from the metal made hemisphere will have its diameter equal to the radius of the hemisphere.

i.e., Diameter of the spherical part, d = r = 2 cm

∴ Radius of the spherical part = $\frac{r}{2}$ = 1 cm

∴ The volume of the spherical part is,

= $\frac{4}{3} \pi (\frac{r}{2} )^3$

= $\frac{4}{3} \pi (1 )^3$

= $\frac{4}{3} \times \frac{22}{7}$

= $\bold{4.19\:cm^3}$

Finding the volume and cost of the remaining part of the metal:

After cutting a maximum spherical part,

The volume of the remaining part of the metal is,

= [Volume of hemisphere] - [Volume of spherical part]

= 16.76 cm³ - 4.19 cm³

= 12. 57 cm³

If the price of 1 cubic centimeter of metal is = Rs. 7

Then,

The price of 12.57 cubic centimeter of metal is,

= Rs. 7 × 12.57 cm³

= Rs. 87.99

≈ Rs. 88

Thus, the price of the remaining part of the metal is → Rs. 88.

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