Sure, let's break it down step by step.
### (b) If the diameter of the base of a cylindrical pipe is 30 cm, find the area of the base of the pipe. [tex]\((\pi=3.14)\)[/tex]
1. Given:
- Diameter of the base of the cylindrical pipe, [tex]\(d = 30\)[/tex] cm
2. Calculate the radius:
[tex]\[
r = \frac{d}{2} = \frac{30}{2} = 15 \text{ cm}
\][/tex]
3. Calculate the area of the base:
[tex]\[
\text{Area of the base} = \pi r^2 = 3.14 \times (15)^2
\][/tex]
[tex]\[
\text{Area of the base} = 3.14 \times 225 = 706.5 \text{ cm}^2
\][/tex]
Therefore, the area of the base of the cylindrical pipe is [tex]\(706.5 \text{ cm}^2\)[/tex].
---
### 7. (a) If the area of the base of a cylindrical tank is 154 sq. ft, find the radius and the circumference of it. [tex]\((\pi=22 / 7)\)[/tex]
1. Given:
- Area of the base of the cylindrical tank, [tex]\(A = 154\)[/tex] sq. ft
2. Calculate the radius:
[tex]\[
A = \pi r^2
\][/tex]
[tex]\[
154 = \frac{22}{7} r^2
\][/tex]
[tex]\[
154 = \frac{22}{7} r^2
\][/tex]
[tex]\[
\Rightarrow r^2 = \frac{154 \times 7}{22} = 49
\][/tex]
[tex]\[
\Rightarrow r = \sqrt{49} = 7 \text{ ft}
\][/tex]
Therefore, the radius of the base of the cylindrical tank is 7 ft.
3. Calculate the circumference:
[tex]\[
C = 2\pi r
\][/tex]
[tex]\[
C = 2 \times \frac{22}{7} \times 7
\][/tex]
[tex]\[
C = 2 \times 22 = 44 \text{ ft}
\][/tex]
Therefore, the circumference of the base of the cylindrical tank is 44 ft.
---
### 7. (b) A circular playground of area [tex]\(153.86\, m^2\)[/tex] is plastered. What is the diameter of the plastered part of the playground? Also, find its circumference. [tex]\((\pi=3.14)\)[/tex]
1. Given:
- Area of the circular playground, [tex]\(A = 153.86 \text{ m}^2\)[/tex]
2. Calculate the radius:
[tex]\[
A = \pi r^2
\][/tex]
[tex]\[
153.86 = 3.14 r^2
\][/tex]
[tex]\[
r^2 = \frac{153.86}{3.14} = 49
\][/tex]
[tex]\[
r = \sqrt{49} = 7 \text{ m}
\][/tex]
Therefore, the radius of the circular playground is 7 m.
3. Calculate the diameter:
[tex]\[
d = 2r = 2 \times 7 = 14 \text{ m}
\][/tex]
Therefore, the diameter of the plastered part of the playground is 14 m.
4. Calculate the circumference:
[tex]\[
C = 2\pi r
\][/tex]
[tex]\[
C = 2 \times 3.14 \times 7 = 43.96 \text{ m}
\][/tex]
Therefore, the circumference of the plastered part of the playground is 43.96 m.
In summary:
- The area of the base of the cylindrical pipe is [tex]\(706.5 \text{ cm}^2\)[/tex].
- The radius and circumference of the cylindrical tank are 7 ft and 44 ft, respectively.
- The diameter and circumference of the plastered part of the playground are 14 m and 43.96 m, respectively.
