Question

A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in figure. The height of the entire rocket is $26cm$, while the height of the conical part is $6cm$. The base of the conical portion has a diameter of $5cm$, while the base diameter of the cylindrical portion is $3cm$. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (Take $\pi =3.14$)

Answer 1

Area to be painted orange $=$ Curved surface area of the cone $+$ Base area of the cone $-$ Base area of the cylinder

Area to be painted yellow $=$ Curved surface area of the cylinder $+$ Area of one bottom base of the cylinder

Curved surface area of cone $=\pi rl$

$l=\sqrt{6^2+{2.5}^2}$

$l=\sqrt{36+6.25}$

$l=\sqrt{42.25}$

$l=6.5cm$

Curved surface area of cone $=3.14\times 2.5\times 6.5$

$=51.025c{m}^2$

Base area of cone $=$ Area of circle

$=\pi r^2$

$=3.14\times (2.5{)}^2$

$=3.14\times 6.25$

$=19.625c{m}^2$

Curved surface area of cylinder $=2\pi rh$

$=2\times 3.14\times 1.5\times 20$

$=188.4c{m}^2$

Base area of cone $=$ Area of circle

$=\pi r^2$

$=3.14\times (1.5{)}^2$

$=7.065c{m}^2$

Area to be painted orange $=$ Curved surface area of the cone $+$ Base area of the cone $-$ Base area of the cylinder

$=51.025+19.625-7.0625$

$=63.59c{m}^2$

Area to be painted yellow $=$ Curved surface area of the cylinder $+$ Area of one bottom base of the cylinder

$=188.4+7.065$

$=195.465c{m}^2$

Hence,

Area to be painted orange $=63.59c{m}^2$

Area to be painted yellow $=195.465c{m}^2$