Question

A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm and 6 cm,respectively. Find the total surface area of the solid.(Use $\pi =3.14)$

Answer 1

Given;

Common diameter of cylinder , hemisphere and cone = 3.5 cm ,

So, radius of cylinder, hemisphere and cone = 1.75 cm

Height of cylinder = 10 cm
Height of cone = 6 cm
As per question;

Volume of solid = Volume of cylinder + Volume of hemisphere + Volume of cone

Volume of cylinder = $\pi$r²h

Volume of cylinder = $\pi$ × $(1.75{)}^2$ × 10

Volume of hemisphere = 2$\pi$r³

Volume of hemisphere = 2× $\pi$ × ($1.75{)}^3$

Volume of cone = $\frac{1}{3}$$\pi$ r²h

Volume of cone = $\frac{1}{3}$$\pi$ × ($(1.75{)}^2$ × 6

Volume of solid =$\pi$ × $(1.75{)}^2$ × 10 + 2× $\pi$ × ($1.75{)}^3$ + $\frac{1}{3}$×$\pi$ × ($(1.75{)}^2$ × 6

Volume of solid = 3.14 × 3.0625× 10 + 2× 3.14 × 5.3593753 + 3.14 × 3.0625 ×63

Volume of solid = 96.1625 + 33.6568753 + 3.14 × 3.0625 × 2

Volume of solid = 96.1625 + 11.2189583 + 19.2325

Volume of solid = 126.6139583 cm³