Question

Find the area and the perimeter of both shapes. explain what you are doing and clearly stating all formulas used.

Answer 1

see below

Explanation:

a) diameter = 5 ⇒ radius (r) = 2.5

area of circle =
`\pi`r² =
`\pi` x 2.5² = 6.25
`\pi` = 19.6 cm² (3 sf)

perimeter = circumference of circle

= 2
`\pi`r = 2 x
`\pi` x 2.5 = 5
`\pi` = 15.7 cm (3 sf)

b) area of sector =
`(\theta)/(360) * \pi r^2`

=
`(300)/(360) *\pi 2^2`

=
`(10)/(3) \pi` = 10.5 cm² (3 sf)

perimeter = circumference - arc length

= 2
`\pi`r -
`(\theta)/(360) *2 \pi r`

= 4
`\pi` -
`(60)/(360) *4 \pi`

=
`(10)/(3) \pi` = 10.5 cm (3 sf)

c) area = largest circle - smallest circle

=
`\pi`3² -
`\pi`2²

= 5
`\pi` = 15.7 cm² (3 sf)

perimeter = circumference of largest circle + circumference of smallest circle

= 2
`\pi` x 3 + 2
`\pi` x 2

= 10
`\pi` = 31.4 cm (3 sf)