Sumit has bought a closed cylindrical dustbin. The radius of the dustbin is ' ' cm and height is '…
Mathematics20246 marksShort answer
Sumit has bought a closed cylindrical dustbin. The radius of the dustbin is '$r$' cm and height is '$h$' cm. It has a volume of $20\pi\text{ cm}^3$.
(a)
Express '$h$' in terms of '$r$', using the given volume.
(b)
Prove that the total surface area of the dustbin is $2\pi r^2 + \frac{40\pi}{r}$
To show: Total surface area = $2\pi r^2 + \frac{40\pi}{r}$
(c)
Sumit wants to paint the dustbin. The cost of painting the base and top of the dustbin is ₹ 2 per $\text{cm}^2$ and the cost of painting the curved side is ₹ 2.5 per $\text{cm}^2$. Find the total cost in terms of '$r$', for painting the outer surface of the dustbin including the base and top.
(d)
Calculate the minimum cost for painting the dustbin.
