Mathematics
Mathematics
Problem
A cylindrical tank, open at both ends, has an external diameter of 2 m and a height of 3 m. Two identical hemispherical domes, each of the same external diameter as the cylinder, are welded to the open ends to form a closed container. The cylinder and the hemispherical domes are made of sheet metal of uniform thickness 5 mm. a. (i) Calculate the volume of metal used in the entire container. Give your answer in cubic metres, correct to three significant figures. b. (ii) The outside of the container (including the domes) is to be painted at the rate of ₹75 per square metre. Find the total cost of painting, correct to the nearest rupee.Intuitive explanation
This is a surface area problem disguised as a real-world container—the key is recognizing what surfaces actually need sheet metal. Since the tank is open at both ends before the domes are welded on, you're not covering those circular openings with flat metal; instead, the domes replace them entirely. Focus on calculating the outer curved surface of the cylinder plus the outer curved surfaces of both hemispheres (which together form a complete sphere), accounting for the uniform thickness to distinguish outer from inner dimensions where needed.
Intuitive explanation
This is a surface area problem disguised as a real-world container—the key is recognizing what surfaces actually need sheet metal. Since the tank is open at both ends before the domes are welded on, you're not covering those circular openings with flat metal; instead, the domes replace them entirely. Focus on calculating the outer curved surface of the cylinder plus the outer curved surfaces of both hemispheres (which together form a complete sphere), accounting for the uniform thickness to distinguish outer from inner dimensions where needed.