Final answer:
The problem requires calculating the surface area of a solid composed of a cylinder with hemispherical ends and determining the cost to polish this area at a given rate.
Step-by-step explanation:
The student's question involves a composite solid made up of a cylinder with hemispherical ends. To find the cost of polishing the surface of this solid, we need to calculate its total surface area and then apply the given cost rate. Since the solid has a total length of 104 cm and a radius of 7 cm for its hemispherical ends, we can deduct the diameter of the hemispheres (2 * 7 cm = 14 cm) twice from the total length to find the height of the cylindrical part, which will be 104 cm - 14 cm - 14 cm = 76 cm.
The surface area of the cylinder (excluding the bases) is given by the formula A = 2πrh, where r is the radius, and h is the height. So, A = 2π * 7 cm * 76 cm. The surface area of one hemisphere is half the surface area of a sphere, which is 2πr², so for both hemispheres it will be 2π * 7² cm². The total surface area is the sum of the cylindrical part and both hemispheres' surfaces. We then convert this area from cm² to dm² (since 1 dm² = 100 cm²) before multiplying by the cost rate of ₹10 per dm² to find the total polishing cost.