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Shalini has to cut out circles of diameter 1 1/4 cm from an aluminium strip of dimensions 8 3/4 cm by 1 1/4 cm. How many full circles can Shalini cut? Also calculate the wastage of the aluminium strip.

Solution:

Given the rectangular dimensions are8 3/4 cm by 1 1/4 cm

Let the number of circles be x

We need to divide 8 3/4 cm by 1 1/4 cm to get number of circles without overlapping

35/4 ÷ 5/4 = 35/5 = 7

Therefore, shalini can cut 7 full circles and the wastage would be the remaining part

Wastage = area of strip - 7 circles area

Wastage = (length × breadth) - (7 × 22/7 × 5/8 × 5/8)

Wastage = 35/4 × 5/4 - 3850/448

Wastage = 175/16 - 8.59

Wastage = 10.93 - 8.59

Wastage = 2.34cm

✦ Try This: Shalini has to cut out circles of diameter 2/3 cm from an aluminium strip of dimensions 7/8 cm by 2/3 cm. How many full circles can Shalini cut? Also calculate the wastage of the aluminium strip.

Given the rectangular dimensions are7/8 cm by 2/3 cm

Let the number of circles be x

We need to divide 7/8 cm by 2/3 cm to get the number of circles without overlapping

7/8 ÷ 2/3 = 7/8 × 3/2 = 21/16 = 1.31~1

Therefore, shalini can cut 1 full circle and the wastage would be the remaining part

Wastage = area of strip - 1 circles area

Wastage = (7/8 × 2/3) - (1 × 22/7 × 1/3 × 1/3)

Wastage = 7/12 - 22/63

Wastage = 0.583 - 0.34

Wastage = 0.24cm

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 1

NCERT Exemplar Class 8 Maths Chapter 1 Problem 142

Shalini has to cut out circles of diameter 1 1/4 cm from an aluminium strip of dimensions 8 3/4 cm by 1 1/4 cm. How many full circles can Shalini cut? Also calculate the wastage of the aluminium strip.

Summary:

Shalini has to cut out circles of diameter 1 1/4 cm from an aluminium strip of dimensions 8 3/4 cm by 1 1/4 cm. There can be 7 full circles can Shalini and the wastage of the aluminium strip is 2.34cm or 2 (11/32)cm

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