The curved surface area of a right circular cylinder of height 56cm is 1408 cm2. Findthe diameter of the base of the cylinder

The formula for the curved surface area (CSA) of a right circular cylinder is given by:

\[
\text{CSA} = 2 \pi r h
\]

where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder, and
- \( \pi \) is a constant approximately equal to 3.1416.

We are given:
- Curved surface area \( \text{CSA} = 1408 \, \text{cm}^2 \),
- Height \( h = 56 \, \text{cm} \).

### Step 1: Use the formula to solve for \( r \).

\[
1408 = 2 \pi r (56)
\]

Simplifying the right-hand side:

\[
1408 = 112 \pi r
\]

Now, solve for \( r \):

\[
r = \frac{1408}{112 \pi} = \frac{1408}{112 \times 3.1416}
\]

\[
r \approx \frac{1408}{351.86} \approx 4 \, \text{cm}
\]

### Step 2: Find the diameter.

The diameter \( d \) is twice the radius:

\[
d = 2r = 2 \times 4 = 8 \, \text{cm}
\]

Thus, the diameter of the base of the cylinder is \( 8 \, \text{cm} \).

Would you like further details on the calculation or have any questions?

Here are some related questions you might find helpful:
1. How do you find the volume of the same cylinder?
2. What is the total surface area of this cylinder?
3. How does the formula for curved surface area change for different shapes?
4. What are the key differences between curved surface area and total surface area?
5. How would the answer change if the height were doubled?

**Tip:** Remember, the diameter is always twice the radius for any circle!

The curved surface area of a right circular cylinder of height 56 cm is 1408 cm². Find the diameter of the base of the cylinder.

Learn how to calculate the diameter of a cylinder with a height of 56 cm and a curved surface area of 1408 cm². Using the formula for the curved surface area (CSA = 2πrh), this detailed solution walks you through finding the radius and diameter. Suitable for students in Grades 6-8.

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