# 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

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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)

=