Question

Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere. The entire top is $5cm$ in height and the diameter of the top is $3.5cm$. Find the area he has to colour (Take $\pi =22/7$)

• A. $37.2c{m}^2$
• B. $30.2c{m}^2$
• C. $49.2c{m}^2$
• D. $39.6c{m}^2$

Answer 1

The correct option is D $39.6c{m}^2$

We have,

Radius of hemispherical portion of the lattu$r=\frac{3.5}{2}=\frac{7}{4}cm$

Radius of the conical portion $r=\frac{3.5}{2}=\frac{7}{4}cm$

Height of the conical portion $h=(5-\frac{3.5}{2})=\frac{13}{4}cm$

Slant height of the conical part $l=\sqrt{r^2+h^2}$

$l=\sqrt{{\left(\frac{7}{4}\right)}^2+{\left(\frac{13}{4}\right)}^2}=\sqrt{\frac{218}{4}}=3.69cm\approx 3.7cm$

Total surface area of the top will be,

$2\pi r^2+\pi rl=\pi r(2r+l)=\frac{22}{7}\times \frac{7}{4}(2\times \frac{7}{4}+3.7)=39.6c{m}^2$