Question

A circular metallic plate of radius 8 cm and thickness 6 mm is melted and molded into a pie (a sector of the circle with thickness) of radius 16 cm and thickness 4 mm. Find the angle of the sector.

Answer 1

Area of the circular plate melted = π(8²) = 64π cm²

Thickness = 6 mm = `6/10` cm

So, volume = area × volume

= `64pi xx 6/10` = V₁

Area of the pie made = `theta/360 xx pi(16^2)`

= `(256pi) theta/360`

Thickness of the pie made = 4 mm

= `4/10` cm

∴ Volume of the pie made = `(256pi) theta/360 xx 4/10` = V₂

We are given V₁ = V₂ 

⇒ `64pi 6/10 = (256pi)(theta/60) xx 4/10`

θ = `64 xx 6/10 xx 1/256 xx 360 xx 10/4`

= 135°

(i.e) θ = `(3pi)/4`