Question

The external and internal radii of a hollow hemispherical vessel are $15\text{cm}$ and $10\text{cm}$ respectively. The approximate cost of painting it at the rate of $₹2$ per $\text{sq. cm}$ is:

• A. $₹4,850$
• B. $₹4,860$
• C. $₹4,870$
• D. $₹4,880$

Answer 1

The correct option is C $₹4,870$

If $r$ is the inner radius, $R$ is the outer radius of the hollow hemispherical vessel, then its total surface area is:
TSA=External CSA + Internal CSA + Area of the cross-section
$=2\pi R^2+2\pi r^2+\pi (R^2-r^2)$
$=3\pi R^2+\pi r^2$
$=\pi (3R^2+r^2)$
Given that $R=15\text{cm}$ and $r=10\text{cm}$, we have:
TSA $=\pi (3\times 225+100)\approx 2,435\text{sq. cm}$
Hence, total cost of painting $\approx 2,435\text{sq. cm}\times ₹2\text{per sq. cm}=₹4,870$