Question

The internal and external diameters of a hollow hemispherical vessel are $24cm$ and $25cm$, respectively. The cost to paint $1{cm}^2$ surface is $Rs.0.05$. Find the total cost to paint the vessel all over. (use $\pi =\frac{22}{7}$)

• A. $Rs.2100$
• B. $Rs.1867$
• C. $Rs.1245$
• D. None of the above

Answer 1

Answer: (D)

None of the above

Internal radius $=r=\frac{24}{2}cm=12cm$
External radius $R=\frac{25}{2}cm$
Surface area of the hollow hemispherical vessel to be painted $=$ Curved surface area of external hemisphere $+$ Curved surface area of internal hemisphere $+$ Area of the top
$=2\pi R^2+2\pi r^2+(\pi R^2-\pi r^2)=3\pi R^2+\pi r^2=3\times \frac{22}{7}\times {\left(\frac{25}{2}\right)}^2+\frac{22}{7}\times {\left(12\right)}^2=\frac{22}{7}[3\times 156.25+144]=1925.78{cm}^2$
Given, cost of painting $1{cm}^2$ surface $=Rs.0.05$
Therefore, cost of painting $1925.78{cm}^2$ surface $=1925.78\times Rs.0.05=Rs.96.28$