Question

A circular pizza of radius 15 cm is to be shared by 6 people consisting of 4 children and 2 adults. pizza is divided equally for individual child and similarly for adults. the area of the piece given to adults is 82.5 square.cm. find the angle contained by pizza slice of child?

Answer 1

Concept:

An angle is a figure produced by two rays that share a common endpoint, known as the vertex of the angle. The area of a circle is $\pi$ times the square of the radius.

Given:

The radius of the pizza = 15 cm.

The number of adults = 2.

The number of children = 4.

The area of the piece given to adults = $82.5 cm^{2}$

Find:

The angle contained by pizza slice of a child.

Solution:

The pieces of pizza will be in form of sectors of the circle.

Let r be the radius of the pizza and $\alpha ,\beta$ be the angle of sectors of adults and children.

The area of the piece given to adults = $82.5 cm^{2}$

$\frac{\alpha}{360} *\pi *r^{2} =82.5$

$\frac{\alpha}{360} *\pi *(15)^{2} =82.5$

$\alpha *3.14 *225=82.5*360$

$\alpha =\frac{82.5*360}{3.14*225}$

$\alpha =\frac{29700}{706.5}$

$\alpha =42$

$2\alpha +4\beta =360$

$\alpha +2\beta =180$

$42+2\beta =180$

$\beta =69$°

Hence the angle contained by the pizza slice of a child is 69°.