Sure, let's solve each part of the given problems step by step.
### Question 5:
(a) If the radius of a circular room is 14 m, then the area it covers can be calculated using the formula for the area of a circle, which is [tex]\( A = \pi r^2 \)[/tex]. Given [tex]\( \pi = \frac{22}{7} \)[/tex] and the radius [tex]\( r = 14 \)[/tex] m:
[tex]\[
A_{\text{room}} = \left(\frac{22}{7}\right) \times (14)^2
\][/tex]
Plugging in the values:
[tex]\[
A_{\text{room}} = \left(\frac{22}{7}\right) \times 196 = 616 \, \text{m}^2
\][/tex]
So, the area of the circular room is [tex]\( 616 \, \text{m}^2 \)[/tex].
(b) If the radius of a circular fun park is 21 m, then the area it covers can be calculated the same way. Given [tex]\( \pi = \frac{22}{7} \)[/tex] and the radius [tex]\( r = 21 \)[/tex] m:
[tex]\[
A_{\text{park}} = \left(\frac{22}{7}\right) \times (21)^2
\][/tex]
Plugging in the values:
[tex]\[
A_{\text{park}} = \left(\frac{22}{7}\right) \times 441 = 1386 \, \text{m}^2
\][/tex]
So, the area of the circular fun park is [tex]\( 1386 \, \text{m}^2 \)[/tex].
(c) A cow is tied with a rope of 7 ft in length, so the radius of the grazing area is 7 ft. Using the same formula [tex]\( A = \pi r^2 \)[/tex] and given [tex]\( \pi = \frac{22}{7} \)[/tex]:
[tex]\[
A_{\text{grazing}} = \left(\frac{22}{7}\right) \times (7)^2
\][/tex]
Plugging in the values:
[tex]\[
A_{\text{grazing}} = \left(\frac{22}{7}\right) \times 49 = 154 \, \text{ft}^2
\][/tex]
So, the grazing area of the cow is [tex]\( 154 \, \text{ft}^2 \)[/tex].
### Question 6:
(a) If the diameter of the base of a cylindrical bowl is 9 cm, then the radius of the base is half of the diameter, which is [tex]\( \frac{9}{2} = 4.5 \)[/tex] cm. Using the formula for the area of a circle [tex]\( A = \pi r^2 \)[/tex] and given [tex]\( \pi = 3.14 \)[/tex]:
[tex]\[
A_{\text{base}} = 3.14 \times (4.5)^2
\][/tex]
Plugging in the values:
[tex]\[
A_{\text{base}} = 3.14 \times 20.25 = 63.585 \, \text{cm}^2
\][/tex]
So, the area of the base of the cylindrical bowl is [tex]\( 63.585 \, \text{cm}^2 \)[/tex].
