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Question

A rocket is in the form of a circular cylinder closed at the lower end with a cone of the same radius attached to the top. The cylinder is of radius 2.5 m and height 21 m and the cone has the slant height 8 m. Calculate the total surface area and the volume of the rocket.


Solution

Curved surface area of cone =πrl=227×2.5×8=62.85 m2

Curved surface area of cylinder =2πrh=2×227×2.5×21=330 m2

Area of the base circle of the cylinder =πr2=227×2.5×2.5=19.64 m2

Hence, total surface area of rocket=62.85+330+19.64=412.5 m2

Now, volume of cylinder =πr2h=227×2.5×2.5×21=412.5 m3

For the cone, l2=h2+r2

82=h2+2.52

h=7.59 m

Volume of the cone =13πr2h=13×227×2.5×2.5×7.59=49.69 m3

Hence, total volume of rocket =412.5+49.69=462.19 m3

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