Find the height of a cylinder whose volume is 5460 cm³ and base is 12 cm wide.

Ops: A. 45.16 cm

B. 51.29 cm

С. 48.26 cm

D. 41.28 

To find the height \( h \) of the cylinder, we can use the formula for the volume of a cylinder:

\[
V = \pi r^2 h
\]

Where:
- \( V \) is the volume of the cylinder (5460 cm³),
- \( r \) is the radius of the base,
- \( h \) is the height.

The diameter of the base is 12 cm, so the radius \( r \) is half of that:

\[
r = \frac{12}{2} = 6 \, \text{cm}
\]

Now, substitute the known values into the volume formula:

\[
5460 = \pi (6)^2 h
\]

\[
5460 = \pi \times 36 \times h
\]

Now solve for \( h \):

\[
h = \frac{5460}{\pi \times 36}
\]

Let's calculate that.

The height of the cylinder is approximately \( 48.27 \, \text{cm} \), which corresponds to option **C. 48.26 cm**.

Would you like more details on this calculation or have any questions?

Here are some related questions for practice:
1. What is the surface area of a cylinder with the same dimensions?
2. How would the height change if the diameter of the base was increased to 14 cm?
3. What would be the volume if the height was increased by 10%?
4. How do you calculate the lateral surface area of a cylinder?
5. How does changing the radius affect the volume of a cylinder?

**Tip:** When solving problems involving cylinders, always check if you're working with the diameter or radius, as it affects the calculations.

Find the height of a cylinder whose volume is 5460 cm³ and base is 12 cm wide.

Learn how to calculate the height of a cylinder with a volume of 5460 cm³ and a base diameter of 12 cm. This problem involves key geometric concepts such as the volume formula V = πr²h. Perfect for students in Grades 8-10, the step-by-step solution explains each stage of the calculation.

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