Question

Q.10. Shalini has to cut out circles of diameter 1 whole 1 upon 4 cm from an aluminium strip of dimensions 8 whole 3 upon 4 cm by 1 whole 1 upon 4 cm. How many full circles can shalini cut? Also, calculate the wastage of the aluminium strip. But, my book answer is, 7 circles, wastage = 2 whole 11 upon 32

Answer 1

Step-by-step explanation:

The answer is given below :

Diameter of a circle,

d = 1 1/4 cm = 5/4 cm

So, radius of each circle,

r = 5/8 cm

Area of each circle,

= π × r²

= π × (5/8)² cm²

= 25π/64 cm²

Now, area of the aluminium strip

= 8 3/4 × 1 1/4 cm²

= 35/4 × 5/4 cm²

= 175/16 cm²

The diameter of the circle = breadth of the strip

So, number of full circles

= length of the strip / diameter of a circle

= (8 3/4) / (1 1/4)

= (35/4) / (5/4)

= 7 [Ans.]

So, area of the seven circles

= 7 × 25π/64 cm²

= 275/32 cm² (put π = 22/7)

So, area wasted

= area of the strip - area of the seven circles

= (175/16 - 275/32) cm²

= 75/32 cm²

2.34375 cm²