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 [tex]\( A \)[/tex] of a circle is:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
For the top of the table:
[tex]\[ r = 60 \, \text{cm} \][/tex]
Substitute the value of [tex]\( r \)[/tex] into the formula:
[tex]\[ A = \pi (60)^2 \][/tex]
[tex]\[ A = \pi \times 3600 \][/tex]
[tex]\[ A \approx 3.14159 \times 3600 \][/tex]
[tex]\[ A \approx 11309.73 \, \text{cm}^2 \][/tex]
Therefore, the area of the top of the table is approximately [tex]\( 11309.73 \, \text{cm}^2 \)[/tex].
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 [tex]\( r \)[/tex] of the base, we need to divide the diameter by 2:
[tex]\[ r = \frac{30}{2} \][/tex]
[tex]\[ r = 15 \, \text{cm} \][/tex]
Using the same area formula [tex]\( A = \pi r^2 \)[/tex]:
For the base of the table:
[tex]\[ r = 15 \, \text{cm} \][/tex]
Substitute the value of [tex]\( r \)[/tex] into the formula:
[tex]\[ A = \pi (15)^2 \][/tex]
[tex]\[ A = \pi \times 225 \][/tex]
[tex]\[ A \approx 3.14159 \times 225 \][/tex]
[tex]\[ A \approx 706.86 \, \text{cm}^2 \][/tex]
Therefore, the area of the base of the table is approximately [tex]\( 706.86 \, \text{cm}^2 \)[/tex].
In summary:
a) The area of the top of the table is approximately [tex]\( 11309.73 \, \text{cm}^2 \)[/tex].
b) The area of the base of the table is approximately [tex]\( 706.86 \, \text{cm}^2 \)[/tex].
