Question

If a circle has a radius of 12 and a sector defined by a 78 degree arc, what is the area, in cm2, of the sector? Round your answer to the nearest tenth.

Answer 1

A = (78/360)*3.14*12^2
A = (78/360) * 3.14 * 144
A = (78/360) * 452.16
A = 97.968 cm^2 = 98.0 cm^2

Answer 2

Required area of the sector of circle is
`97.97cm^2`

Explanation:

We have given angle
`78^(\circ)` and radius is 12

We have formula for area of the sector of a circle is
`(\theta)/(360)\cdot \pi\cdot r^2`

Here,
`\theta=78^(\circ)`

`r=12`

On substituting the values we will get

`Area=(78^(\circ))/(360)\cdot \pi\cdot {12}^2`

Using
`\pi=3.14`

`\Rightarrow Area=(78^(\circ))/(360)\cdot3.14\cdot 144`

After simplification we will get

`\Rightarrow Area=(35268.48)/(360)`

After further simplification we will get

`\Rightarrow Area=97.968=97.97`