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Explain Bot To find the surface area of a cylinder, you need to calculate the area of the two circular bases and the area of the curved surface.
1. To find the area of the circular bases, use the formula for the area of a circle: A = π * r^2, where π is approximately 3.14159 and r is the radius.
In this case, the radius (r) is given as 7. Therefore, the area of each circular base is A_base = π * 7^2.
2. The curved surface of a cylinder is basically a rectangle that has been rolled up to form a tube. The length of this rectangle is equal to the circumference of the circular base, and the width is equal to the height of the cylinder.
The circumference of a circle can be found using the formula: C = 2 * π * r, where C is the circumference and r is the radius.
In this case, the radius (r) is given as 7. Therefore, the circumference is C = 2 * π * 7.
The curved surface area (A_curved) is calculated by multiplying the circumference (C) by the height (h) of the cylinder: A_curved = C * h.
3. Once you have the areas of the two circular bases (A_base) and the curved surface (A_curved), you can find the total surface area of the cylinder by adding them together: A_total = 2 * A_base + A_curved.
Now, let's calculate the surface area of the cylinder with a radius of 7 and a height of 8:
Calculating the area of the circular bases:
A_base = π * 7^2
= 3.14159 * 49
≈ 153.93804
Calculating the circumference:
C = 2 * π * 7
= 2 * 3.14159 * 7
≈ 43.9823
Calculating the curved surface area:
A_curved = C * h
= 43.9823 * 8
≈ 351.8584
Calculating the total surface area:
A_total = 2 * A_base + A_curved
= 2 * 153.93804 + 351.8584
≈ 659.7345
Therefore, the surface area of the cylinder with a radius of 7 and a height of 8 is approximately 659.7345 square units.