A cylinder has a height of 10 cm and a volume of 200π cm³. What is the radius of

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Question: A cylinder has a height of 10 cm and a volume of 200π cm³. What is the radius of the base?

Options:

Correct Answer: 5 cm

Solution:

Using the volume formula V = πr²h, we have 200π = πr²(10). Thus, r² = 20, so r = √20 = 4.47 cm.

A cylinder has a height of 10 cm and a volume of 200π cm³. What is the radius of the base?

A cylinder has a height of 10 cm and a volume of 200π cm³. What is the radius of the base?

Step 1: Write down the formula for the volume of a cylinder, which is V = πr²h.
Step 2: Substitute the known values into the formula. We know the volume (V) is 200π cm³ and the height (h) is 10 cm. So, we write 200π = πr²(10).
Step 3: Simplify the equation. Divide both sides by π to get 200 = r²(10).
Step 4: Now, divide both sides by 10 to isolate r². This gives us r² = 20.
Step 5: To find the radius (r), take the square root of both sides. So, r = √20.
Step 6: Calculate the square root of 20. This gives us r ≈ 4.47 cm.

Volume of a Cylinder – Understanding the formula for the volume of a cylinder, V = πr²h, where r is the radius and h is the height.
Algebraic Manipulation – Ability to rearrange equations to solve for an unknown variable, in this case, the radius.