Question

What is the value of S if r = 2.45 and h = 5.13 in the equation S = 2πr² + 2πrh?

A) 98.4
B) 78.3
C) 116.6
D) 64.2

Answer 1

The value of S calculated using the given formula S = 2πr² + 2πrh with r = 2.45 and h = 5.13, and rounded to three significant figures, is S = 305, which is not listed in the provided multiple-choice options.

Step-by-step explanation:

Given the equation S = 2πr² + 2πrh, we will calculate the value of S with r = 2.45 and h = 5.13. First, we calculate the term 2πr², which represents the area of the two circular bases of a cylinder; then the term 2πrh, which represents the area of the cylindrical side surface (the lateral area).

Performing the calculations step by step:

• For 2πr²: 2 * 3.14159 * (2.45)² = 37.69911 * 6.0025 = 226.194
• For 2πrh: 2 * 3.14159 * 2.45 * 5.13 = 6.28318 * 12.5665 = 78.956
• Adding both values together for S: 226.194 + 78.956 = 305.15

Since we need to be consistent with the significant figures provided in the inputs, we round the answer to three significant figures, giving us S = 305.

The correct option that matches our calculated value is not listed in the given options. Therefore, all the provided options (A) 98.4, (B) 78.3, (C) 116.6, and (D) 64.2 are incorrect.

Answer 2

C) 116.6

Step-by-step explanation:

What is the value of S if r = 2.45 and h = 5.13 in the equation

S = 2πr² + 2πrh

S = 2π(2.45)² + 2π(2.45)*(5.13)

S = 2π*(2.45)*(2.45 + 5.13) [Factor out 2π*(2.45)]

S = 2π*(2.45)*(7.58)

S = 2*(3.14)*(2.45)*(7.58)

S = 116.626 or 116.6 to 4 sig figs