A cylinder has a volume of 100π cm³ and a height of 10 cm. What is the radius of

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Question: A cylinder has a volume of 100π cm³ and a height of 10 cm. What is the radius of the base?

Options:

Correct Answer: 4 cm

Solution:

Volume = πr²h. Therefore, 100π = πr²(10) => r² = 10 => r = √10 ≈ 3.16 cm.

A cylinder has a volume of 100π cm³ and a height of 10 cm. What is the radius of the base?

A cylinder has a volume of 100π cm³ and a height of 10 cm. What is the radius of the base?

Step 1: Write down the formula for the volume of a cylinder: Volume = πr²h.
Step 2: Substitute the known values into the formula. We know the volume is 100π cm³ and the height is 10 cm, so we write: 100π = πr²(10).
Step 3: Simplify the equation by dividing both sides by π. This gives us: 100 = r²(10).
Step 4: Now, divide both sides by 10 to isolate r²: 100 / 10 = r², which simplifies to 10 = r².
Step 5: To find the radius r, take the square root of both sides: r = √10.
Step 6: Calculate the approximate value of √10, which is about 3.16 cm.

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