Question

1. b. a cylindrical and its dimensions are shown in the diagram.

which measurement is closest to the lateral surface area of the cylinder in square centimeters?
f. 575.3 cm²
g. 287.6 cm²
h. 340.4 cm²

Explanation:

Step1: Recall lateral surface area formula

The formula for the lateral (or curved) surface area of a cylinder is \( LSA = 2\pi rh \), where \( r \) is the radius and \( h \) is the height. First, we need to find the radius from the given diameter. The diameter \( d = 8.4 \, \text{cm} \), so the radius \( r=\frac{d}{2}=\frac{8.4}{2}=4.2 \, \text{cm} \), and the height \( h = 12.9 \, \text{cm} \).

Step2: Substitute values into the formula

Substitute \( r = 4.2 \), \( h = 12.9 \), and \( \pi \approx 3.14 \) into the formula:
\( LSA = 2\times3.14\times4.2\times12.9 \)

Step3: Calculate step by step

First, calculate \( 2\times3.14\times4.2 \):
\( 2\times3.14 = 6.28 \)
\( 6.28\times4.2 = 26.376 \)

Then, multiply by \( 12.9 \):
\( 26.376\times12.9 \approx 26.376\times13 - 26.376\times0.1 = 342.888 - 2.6376 = 340.2504 \, \text{cm}^2 \)

Answer:

H. \( 340.4 \, \text{cm}^2 \)