Question

find the circumference and area of the semicircle whose diameter is 8.4​

Answer 1

Answer:

circumference= 2πr/2+d

πr+d=πx4.2+8.4=21.6cm

Area = πr 2 = πx4.2^2 = 20.78cm2

Answer 2

Given:

The diameter of a semicircle is 8.4 units.

To find:

The circumference and area of the semicircle.

Solution:

To answer this question, first of all, we should know that in a circle having radius 'r', the circumference and area of the circle are given by:

$Circumference = 2\pi \: r$

$Area = \pi \: {r}^{2}$

So,

The circumference of the semicircle is given by

$\frac{2\pi \: r}{2} + 2r = \pi r + 2r$

The area of the semicircle is given by

$\frac{ {\pi \: r}^{2} }{2}$

Now, as given, we have,

The diameter of the semicircle = 8.4 units.

So,

The radius of the semicircle = 8.4/2 = 4.2 units.

Hence,

The circumference of the semicircle is

$= \: \pi \: r + 2r = (\frac{22}{7} \times 4.2) + (2 \times 4.2) = 22 \times 0.6 + 8.4 = 13.2 \:+ 8.4 = 21.6 units$

Now,

The area of the semicircle is

$= \frac{ {\pi \: r}^{2} }{2} = \frac{22 \times {(4.2)}^{2} }{7 \times 2}$

$= 11 \times 0.6 \times 4.2$

$= 27.72 \: square \: units$

Hence, the circumference and area of the semicircle having a diameter of 8.4 units are 21.6 units and 27.72 square units respectively.