The shape below is formed from a cone joined to a
hemisphere.
The cone and the hemisphere have the same curved
surface area.
The volume of this shape can be written in the form
3pi cubed/a (b+√√3) cm³.
Calculate the values of a and b.



Answer :

Answer:

To calculate the values of ( a ) and ( b ), we can compare the formulas for the curved surface area of a cone and a hemisphere, and the volume of the shape given.

The curved surface area of a cone is given by ( \pi rl ), where ( r ) is the radius of the base of the cone and ( l ) is the slant height.

The curved surface area of a hemisphere is half the surface area of a sphere, which is ( 2\pi r^2 ).

Given that the cone and hemisphere have the same curved surface area, we can equate the two formulas:

[ \pi rl = 2\pi r^2 ] [ rl = 2r ] [ l = 2 ]

The volume of the shape can be written as ( \frac{1}{3} \pi r^2 h + \frac{2}{3} \pi r^3 ), which simplifies to ( \frac{1}{3} \pi r^2 (2r) + \frac{2}{3} \pi r^3 = \frac{2}{3} \pi r^3 (1 + \sqrt{3}) ).

Comparing this with the given form:

[ a = 2 ] [ b + \sqrt{\sqrt{3}} = 1 + \sqrt{3} ] [ b = 1 ]

Therefore, the values of ( a ) and ( b ) are:

( a = 2 )

( b = 1 )

hope it helps please mark me as brainliest thanks