Question

a toy rocket of height 26cm is in the shape of a cylinder of base diameter 3cm surmounted by a cone of height 6cm with base radius 2.5cm. find the TSA of the toy

Answer 1

height of cylinder = total height - height of cone 26-6 = 20cm

TSA of the cylinder seperately = 2πr(r+h)
= 2π*3*(3+20)
= 6*23π
= 138π sq.cm
But some of the top surface of the cone is covered with the cone's.
∴ Actual TSA = 138π-(πr²-π(radius of cone)²)
= 138π-π((3)²-(2.5²))
= 138π - 2.75π
= 135.25π sq.cm

The diameter of the cone is completely covered by the cylinder's.
∴ Actual TSA of cone = CSA of cone
= πrl

Now, l = √[(r)²+(h)²]
= √[(2.5)²+(6)²]
= √[6.25+36]
= √42.25
= 6.5cm

∴ CSA = π*2.5*6.5 = 16.25π sq.cm

Therefore TSA of total figure
= 135.25π+16.25π 
= 151.5π
= 151.5(22/7)
= 476.14 sq.cm