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.

Answer 1

Radius of the cylinder portion (r) = 2.5 m 

Height of the cylinder portion (h) = 21 m 

∴ Surface area of the cylindrical portion = 2πrh 

= 2 × \(\frac{22}7\) × 2.5 × 21 m 

= 330 m ………(1) 

Radius of the conical portion (r) = 2.5 m 

Slant height of the conical portion (l) = 8 m 

∴ Curved surface area of the conical portion = πrl 

= (\(\frac{22}7\)) × 2.5 × 8 m 

= 62.86 m ……..(2) 

Area of the circular top = πr²

= (\(\frac{22}7\)) × 2.5 × 2.5 m² 

= 19.64 m² ……………(3) 

∴ Total surface area of the rocket 

= (330 + 62.86 + 19.64) m² 

[From (1) , (2), (3)] 

= 412.5 m² 

Volume of the cylindrical portion = πr²h

= \(\frac{22}7\) x (2.5)² x 21

= 412.5 m²