Question

From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid.

Answer 1

We have, 

the height of the cone = the height of the cylinder = h =2.8 cm and the radius of the base, r = `4.2/2 = 2.1  "cm"`

The slant height of the cone, `l = sqrt(r^2 + h^2)`

`=sqrt(2.1^2 + 2.8^2)`

`= sqrt(4.41 +7.84)`

`=sqrt(12.25)`

= 3.5 cm

Now, the total surface area of the remaining solid = CSA of cylinder + CSA of cone + Area of base 

`= 2pirh + pirl + pir^2`

`=pir (2h +l +r)`

`= 22/7 xx2.1xx(2xx2.8xx3.5+2.1)`

`= 22xx0.3xx(5.6+5.6)`

`=6.6xx 11.2`

`= 73.92  "cm"^2`

So, the total surface area of the remaining solid is 73.92 cm².