Question

Kareem cuts 12 identical circles of pastry form a 30cm by 40cm sheet. Find the area of pastry {which remains}

Answer 1

258 cm²

Explanation:

A = 40*30 = 1200 cm²

Ac = 12×πr² = 12×3.14×25 = 942 cm²

Apwr = A - Ac = 1200cm² - 942cm² = 258 cm²

Answer 2

Exact Area = 1200 - 300pi square cm

Approximate Area = 257.522203923062 square cm

Work Shown:

The area of the rectangle is 40*30 = 1200 square cm

Note how we have 4 circles along the horizontal dimension which is 40 cm, so each diameter is 40/4 = 10 cm, and the radius is 10/2 = 5 cm

Each circle has an area of pi*r^2 = pi*5^2 = 25pi

There are 4*3 = 12 circles, so the circle areas combine to 12*25pi = 300pi

Using a calculator, we find that 1200 - 300pi = 257.522203923062 approximately. Round this however you need to.