Question

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Answer 1

Answer: P=20 cm S=75 cm²

Explanation:

We have 2 semicircles with diameter d=10 cm and 1 semicircle with diameter D=20 cm

`\displaystyle\\The\ length \ of \ the\ circle\ is\ \pi D\\The\ length\ of \ the\ semicircle \ is\ (\pi D)/(2)`

`\displaystyle\\a)\\P=2*(\pi d )/(2) +(\pi D)/(2) \\\\P=\pi d+(\pi D)/(2) \\\\P=\pi *(d+(D)/(2) )\\P=\pi *(10+(20)/(3) )\\\\P=\pi *(10+10)\\\\P=20\pi \ cm\\\\`

`b)\\\displaystyle\\The\ area \ of \ the\ circle\ is\ (\pi D^2)/(4) \\The\ area\ of \ the\ semicircle \ is\ (\pi D^2)/(8)\\\\S=2*(\pi d^2)/(8) +(\pi D^2)/(8) \\\\S=\frac{2*\pi *10^2}8} +(\pi *20^2)/(8) \\\\S=(2*\pi*100 )/(8) +(\pi *400)/(8) \\\\S=(200\pi )/(8)+(400\pi )/(8) \\\\S=(600\pi )/(8) \\\\S=75\pi \ cm^2`

Answer 2

(a)20π

(b)74π

Explanation:

(a) 2π(5) + (2π(10) × 1/2) = 2π(5) + 2π(5)

= 2π(10)

= 20π

(b) π(5)^2 + (π(10)^2 × 1/2) = 25π + 50π

=75π