Question

A cubical box of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have ? Find the cost of painting the total surface area of the solid so formed at the rate of ₹5 per 100 sq. cm

Answer 1

Introducing the problem:

surmounted = to be placed on top of.

(Try drawing a diagram to help visualize this scenario. It can be incredibly helpful!)

So with the given info, we know that the hemisphere is placed on top of the cubical box.

Hence, the largest possible diameter is 10 cm.

to find the tsa

tsa of cube = 6$s^{2} = 6*10^{2}$

but one of the faces is covered by the hemisphere.

hence tsa  of object = 6$s^{2} - [tex]s^{2}  + [tex]2\pi r^{2}$ (tsa of hemisphere)

tsa answer: (5*100) + (3.14*10*10*2) = 500 + 628 = 1128 $cm^{2}$

to find the rate:

tsa * rate = 1128 * 5/100 = 56.4 Rs.

Hope this helps :)