Question

Maths Question. Plsss Help. 

 

Answer 1

i)

Find the value  of y.

The height of the original cone was 24 cm and the base has a radius of 12 cm, therefore the radius r at any height y measured from the base must be
r = (24 - y)/2
6 = (24 - y)/2
12 = 24 - y
y = 12

So height of the hemisphere is 12 cm.

ii)

Find the volume of the solid.

V = V Frustum + V Hemisphere

V Frustum = (πh/3)(R²+r²+Rr)

                =π(12)/3)(12²+6²+(12)(6))

               =1008π

V Hemisphere =(2/3)πr³

                      =(2/3)π(6)³

                      =144π

V =1008π+144π

   = 1152π cm³

So volume of the solid is 1152π cm³

Answer 2

iii)

Find the surface area of the solid.

S= S Frustum + S Hemisphere

S Frustum = (π(R+r))√((R-r)²+h²)

                =π(12+6))√((12-6)²+12²)

               = 241.5π

S Hemisphere =3πr²

                      =(3)π(6)²

                      =108π
S =241.5π+108π

   = 349.5π cm²

So surface area of the solid is 349.5π cm²