Geometry homework please help🙏😬

Question

A rectangular pizza, 40cm by 60cm is cut into 24 sqaure pieces. Two round pizzas, each cut into 12 slices, aslo give 24 pieces. So that the pizzas are the same size. What must be the diameter of the round pizzas?

Answer 1

Let's first calculate the size of each of the cut square piece.

From the rectangular pizza,

Total pizza area = 40 cm x 60 cm = 2400 sq cm (which is cut into 24 pieces)

So each square piece has the area = 2400 / 24 = 100 sq cm

Turning to the round pizza, since each round pizza is cut into 12 pieces, we need 1/12th the area of a round pizza to equal that of the cut square piece. Let's assume the round pizza has a radius "R".

Therefore,

Round Pizza's Area = Pi * R²

So each piece of the round pizza = 1/12 * Pi * R² which needs to be equal to 100 sq cm

From this we can calculate R,

R² = 12*100/Pi

Using Pi = 22/7

R² = 381.82 sq cm

Therefore R = sqrt(381.82) = 19.54 cm

Hence, the diameter of each of the round pizza has to be 2 x R = 39.08 cm (answer)

Answer 2

CORRECTION: So that the pieces are the same size

One round pizza accounts for 1/2 the total area: (1/2)(40cm)(60cm) = 1200 cm²

The area of a circle is ∏r², or ∏(d/2)² or ∏d²/4

∏d²/4 = 1200 cm² [one circle]

d² = 4800/∏ cm²

d = 39.1 cm

Check:

r = 19.55

A = 40*60 = 2400 cm²

A = 2*∏r² = 2*3.14*(19.55)² =- 2400.23 (close enough)