Question

The difference between the total surface area and curved surface area of a cylinder of base radius 10 cm is _________.

Answer 1

Let r and h be the radius and height of the cylinder, respectively.

r = 10 cm (Given)

Total surface area of the cylinder = 2$\mathrm{\pi }$r(r + h)

Curved surface area of the cylinder = 2$\mathrm{\pi }$rh

∴ Difference between the total surface area and curved surface area of the cylinder

= Total surface area of the cylinder − Curved surface area of the cylinder

= 2$\mathrm{\pi }$r(r + h) − 2$\mathrm{\pi }$rh

= 2$\mathrm{\pi }$r² + 2$\mathrm{\pi }$rh − 2$\mathrm{\pi }$rh

= 2$\mathrm{\pi }$× (10 cm)² (r = 10 cm)

= 2$\mathrm{\pi }$× 100 cm²

= 200$\mathrm{\pi }$ cm²

Thus, the difference between the total surface area and curved surface area of a cylinder of base radius 10 cm is 200$\mathrm{\pi }$ cm².

The difference between the total surface area and curved surface area of a cylinder of base radius 10 cm is ___200$\mathrm{\pi }$ cm²___.