Question

A paper cone of height 8 cm and base diameter of 12 cm is opened to form a sheet of paper. If a rectangle of dimensions 13 cm × 11 cm is cut from this paper sheet, find the area of the remaining sheet of paper. Use π = 3.14.

• A. $$7.72cm^2$$
• B. $$45.4cm^2$$
• C. $$83.08cm^2$$
• D. $$158.44cm^2$$

Answer 1

Answer:

$$45.4cm^2$$

Base radius of cone = $\frac{12}{2}$ = 6 cm

As we know, slant height (l), base radius (r) and height (h) of cone are related as,

⇒ l² = h² + r²

⇒ l² = 8² + 6² = 64 + 36 = 100

⇒ l = √100 = 10 cm

Now,

Area of paper sheet = Curved surface area of cone

∵ Curved surface area of cone = π $\times$ base radius $\times$ slant height = πrl

⇒ Area of paper sheet = 3.14 $\times$ 6 $\times$ 10 = 188.4 cm²

∵ Area of paper sheet cut = Area of rectangle = 13 $\times$ 11 = 143 cm²

∴ Area of remaining sheet = 188.4 – 143 = 45.4 cm²