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.
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Answer:
There is a mistake in this question. The slant height of the cone should be 8 m instead of 8 cm.
Curved surface area of cone = πrl
= 22/7*2.5*8
= 440/7
= 62.86 sq m
Curved surface area of cylinder = 2πrh
= 2*22/7*2.5*21
= 330 sq m
Area of the base circle of the cylinder = πr²
= 22/7*2.5*2.5
= 19.64 sq m
Total surface area of rocket = 62.85 + 330 + 19.64
= 412.5 sq m
Volume of cylinder = πr²h
= 22/7*2.5*2.5*21
= 412.5 cu m
Now
h² = 8² - (2.5)²
h² = 64 - 6.25
h² = 57.75
h = √57.75
h = 7.6 m
Volume of the cone = 1/3πr²h
= 1/3*22/7*2.5*2.5*7.6
= 49.76 cu m
Total volume of rocket = 412.5 + 49.76
= 462.26 cu m
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