Question

a circular mirror of radius 21 cm surronded by a circular frame of width 3.5 cm.find the cost of making the frame at RS 1.50 per cm square

Answer 1

let  radius of mirror [r] = 21 cm

circular frame of width 3.5 cm

∴radius of mirror + frame [R] = [21 cm +3.5cm] =24.5cm

Now area of the frame= The area of the region enclosed by two concentric circles is given by:-  A = π (R^2 – r^2)  Here, R = 24.5cm, r = 21 cm and π = 3.14

A = π (R^2 – r^2)  = π (R – r)(R + r) cm^2

[applying (a^2 – b^2) = (a – b)(a + b)] identity

A = π (24.5^2 – 21^2)  = 22/7 (24.5 – 21)(24.5 + 21)  cm^2

A = π (24.5^2 – 21^2) = 22/7 *3.5*45.5  cm^2

A =22*0.5*45.5 =500.5 cm^2

cost of making frame for 1cm is 1.50

⇒total cost Rs 500.5 cm^2 *1.50 =Rs 750.75

Therefore rupees needed for framing the mirror=Rs 750.75 ANS

Answer 2

The area of the region enclosed by two concentric circles is A = π (R2 – r2)

Here, R = 24.5cm, r = 21 cm and π = 22/7

So Area, A = 22/7 (600.25 – 441) sq cm = 22/7 (159.25) sq cm = 500.5q. cm.

cost of making the frame at RS 1.50 per cm square =500.5* RS 1.50

=RS 750.75 ans