Question

Rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diametre and height of the cylinder are 9cm and 15 cm .

If the slant height of the conical portion is 7.5 find the total surface area and volume

Answer 1

Curved surface area of cone = πrl

= 22/7*4.5*7.5

= 106.07 sq m

Curved surface area of cylinder = 2πrh

= 2*22/7*4.5*15

= 424.28 sq m

Area of the base circle of the cylinder = πr²

= 22/7*4.5*4.5

= 63.64 sq m

Total surface area of rocket = 106.07 + 424.28+ 63.64

= 593.99 sq m

Volume of cylinder = πr²h

= 22/7*4.5*4.5*15

= 954.64 cu m

Now

h² = (7.5)² - (4.5)²

h² = 56.25 - 20.25

h² = 36

h = √ 36

h = 6m

Volume of the cone = 1/3πr²h

= 1/3*22/7*4.5*4.5*6

= 127.28 cu m

Total volume of rocket = 954.64 + 127.28

= 1,081.92 cu m