A cylinder of height 12 cm and radius 5cm is made of cardboard. Use the value of 22
7
for π to calculate the total area of cardboard needed to make:
(a) A closed cylinder
area of top = pi R^2
area of bottom = pi R^2
area of side = 2 pi R h
so
2 pi R^2 + 2 pi R h
= 2 pi R (R + h)
To calculate the total area of cardboard needed to make a closed cylinder, we need to find the combined area of the two circular bases and the lateral surface area.
1. The area of a circular base can be calculated using the formula A = πr^2, where r is the radius.
Given that the radius (r) is 5 cm, we can substitute it into the formula:
A_base = π * (5 cm)^2
2. The lateral surface area can be calculated using the formula A = 2πrh, where r is the radius and h is the height.
Given that the radius (r) is 5 cm and the height (h) is 12 cm, we can substitute the values into the formula:
A_lateral = 2π * (5 cm) * (12 cm)
3. To find the total area, we need to sum the areas of the bases and the lateral surface.
A_total = 2 * A_base + A_lateral
Now let's calculate the area:
A_base = π * (5 cm)^2
= 22/7 * 5 cm * 5 cm
= 22/7 * 25 cm^2
= 550/7 cm^2 (approx. 78.57 cm^2)
A_lateral = 2π * (5 cm) * (12 cm)
= 2 * 22/7 * 5 cm * 12 cm
= 44/7 * 5 cm * 12 cm
= 2640/7 cm^2 (approx. 377.14 cm^2)
A_total = 2 * A_base + A_lateral
= 2 * 78.57 cm^2 + 377.14 cm^2
= 157.14 cm^2 + 377.14 cm^2
= 534.28 cm^2 (approx. 534.3 cm^2)
Therefore, the total area of cardboard needed to make a closed cylinder is approximately 534.3 cm^2.