Question

Factor the expression used for finding the surface area of a cylinder: 2π + 2r - h.

- A. (2π + 2r) - h
- B. 2(π + r - h)
- C. (2 + r)π - h
- D. 2(π - h + r)

Answer 1

The correct answer is option B, 2(π + r - h). The expression is factored by taking 2 as a common factor from the first two terms while leaving h as it is.

Step-by-step explanation:

The correct answer is option B, which is 2(π + r - h). To factor the expression for finding the surface area of a cylinder, look for common factors in each term. The original expression given, 2π + 2r - h, contains the common factor of 2 in the first two terms. Factoring out the 2 gives us 2(π + r) - h. However, since h does not have a factor of 2, we leave it as is, which results in the factored form of 2(π + r - h). This expression represents the multiplication of 2 with the sum of π, r, and -h.

To find the surface area of a cylinder, we use the formula:

Surface Area = 2πr + 2rh

Comparing this with the expression given: 2π + 2r - h, we see that option D, 2(π - h + r), is the correct factorization.

When we factor out 2 from the expression, we get: 2(π + r) - h. This matches the form of the surface area formula, so it is the correct factorization.