Let's break down the problem into two parts and solve each part step-by-step.
Part (a): Work out the area of the top of the table.
Given:
- The radius of the top of the table is 60 cm.
The formula to find the area \(\( A \)\) of a circle is:
\(\[ A = \pi r^2 \]\)
where \(\( r \)\) is the radius of the circle.
For the top of the table:
\(\[ r = 60 \, \text{cm} \]\)
Substitute the value of \(\( r \)\) into the formula:
\(\[ A = \pi (60)^2 \]\)
\(\[ A = \pi \times 3600 \]\)
\(\[ A \approx 3.14159 \times 3600 \]\)
\(\[ A \approx 11309.73 \, \text{cm}^2 \]\)
Therefore, the area of the top of the table is approximately \(\( 11309.73 \, \text{cm}^2 \)\).
Part (b): Work out the area of the base of the table.
Given:
- The diameter of the base of the table is 30 cm.
To find the radius \(\( r \)\) of the base, we need to divide the diameter by 2:
\(\[ r = \frac{30}{2} \]\)
\(\[ r = 15 \, \text{cm} \]\)
Using the same area formula \(\( A = \pi r^2 \)\):
For the base of the table:
\(\[ r = 15 \, \text{cm} \]\)
Substitute the value of \(\( r \)\) into the formula:
\(\[ A = \pi (15)^2 \]\)
\(\[ A = \pi \times 225 \]\)
\(\[ A \approx 3.14159 \times 225 \]\)
\(\[ A \approx 706.86 \, \text{cm}^2 \]\)
Therefore, the area of the base of the table is approximately \(\( 706.86 \, \text{cm}^2 \)\).
In summary:
a) The area of the top of the table is approximately \(\( 11309.73 \, \text{cm}^2 \)\).
b) The area of the base of the table is approximately \(\( 706.86 \, \text{cm}^2 \)\).
