The circumference of the base of a right circular cylinder is 176 cm. Its height is 1 m. Find the lateral surface area of the cylinder.

Question

High School

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Answer :

ramaannira ramaannira · Answer 1 · 2024-10-29T09:20:25-04:00

The lateral surface area of the cylinder is approximately 17584 square centimeters.

Let's solve this step by step.

1. Find the Radius (r) of the Cylinder:

The circumference (C) of the base of the cylinder is given by the formula: [tex]$ C = 2\pi r $[/tex]

Given [tex]$ C = 176 $[/tex] cm, we can rearrange the formula to solve for [tex]$ r $[/tex]:

[tex]\[ 176 = 2\pi r \][/tex]

[tex]\[ r = \frac{176}{2\pi} \][/tex]

[tex]\[ r \approx\frac{176}{6.28} \][/tex]

[tex]\[ r \approx 28.0 \] cm[/tex]

2. Find the Lateral Surface Area (LSA) of the Cylinder:

The lateral surface area of a cylinder is given by the formula: [tex]$ LSA = 2\pi rh $[/tex]

Given [tex]$ h = 1 $[/tex] m and we've just found [tex]$ r = 28.0 $[/tex] cm, we'll convert the height to cm:

[tex]\[ h = 1 \, \text{m} \times 100 \, \text{cm/m} \][/tex]

[tex]\[ h = 100 \, \text{cm} \][/tex]

Now, plug in the values into the formula:

[tex]\[ LSA = 2\pi \times 28.0 \times 100 \][/tex]

[tex]\[ LSA = 5600\pi \][/tex]

3. Calculate the Numerical Value of the LSA:

[tex]\[ LSA \approx 5600 \times 3.14 \][/tex]

[tex]\[ LSA \approx 17584 \, \text{cm}^2 \][/tex]

So, the lateral surface area of the cylinder is approximately [tex]$ 17584 \, \text{cm}^2 $[/tex].