The radius of the base of a cylinder is 4x cm is 27 cm and its height is 33 cm. Find the surface area of the cylinder in terms of 3.14
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To find the surface area of a cylinder, we to calculate the areas of the two circular bases and the lateral surface area.
1. The area of each circular base is given by the formula A = πr^2, where r is the radius.
- In this case, the radius of the base is 4x cm, so the area of each base is A_base = π(4x)^2.
2. The lateral surface area (the curved surface of the cylinder) can be found using the formula A = 2πrh, where r is the radius of the base and h is the height of the cylinder.
- In this case, the radius of the base is 4x cm and the height is 33 cm, so the lateral surface area is A_lateral = 2π(4x)(33).
Now we can calculate the surface area by summing the areas of the two bases and the lateral surface area:
A_surface = 2A_base + A_lateral
= 2(π(4x)^2) + 2π(4x)(33)
= 2π(16x^2) + 2π(132x)
= 32πx^2 + 264πx
So, the surface area of the cylinder in terms of π is 32πx^2 + 264πx.