Find the Volume
Step 1: Find height (h) using h² + r² = s².
Step 2: Find Volume using V = ⅓πr²h.
Cone Slant Challenge!
Use slant height and radius.
Volume of Cone (Slant Height) Game
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This Volume of Cone (Slant Height) Game is a great way to put your skills to the test in a fun environment. By practicing, you’ll start to work out the answers efficiently.
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Volume of Cone (Slant Height) Game
When you’re given the slant height (l) and the radius (r) of a cone, you must first calculate the perpendicular height (h) using the formula h2 = l2 - r2. Then, the volume (V) of a cone is found by taking one-third of the area of its circular base (B) times its perpendicular height (h).
Scroll down the page for a more detailed explanation.
In this game, you may select “Find Volume”, “Find Vertical Height”, or “Mixed Questions”. If you give a wrong answer, the game will provide the correct answer.
Score: 0 / 0
How to Play the Volume of Cone (Slant Height) Game
In the game, you need to find the volume of a cone given the slant height or find the vertical height given the slant height.
Here’s how to play:
- Choose your challenge: Select “Find Volume”, “Find Vertical Height”, or “Mixed Questions”.
- Find Volume: Calculate volume given the radius and slant height.
- Find Vertical Height: Calculate vertical height given the slant height and the radius.
- Enter Your Answer: Enter in the answer.
- Check Your Work: Click the “Check” button (or press the Enter key). The game will tell you if you’re correct. If you are wrong, you will be shown the correct answer.
- Get a New Problem: Click the “Next” button for a new problem.
Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried. - Back to Menu Click “Menu” to restart the game.
Find the Volume of a Cone (Slant Height)
When you’re given the slant height (l) and the radius (r) of a cone, you must first calculate the perpendicular height (h) before you can find the volume.
Here is the complete method, using the Pythagorean Theorem and the Volume formula.
Step 1: Find the Perpendicular Height (h)
The relationship between the radius (r), the perpendicular height (h), and the slant height (l) in a cone always forms a right-angled triangle.
This allows us to use the Pythagorean theorem: a2 + b2 = c2.
r2 + h2 = l2
To solve for the height (h), we rearrange the formula:
\(h = \sqrt{l^2 - r^2}\)
Step 2: Calculate the Volume (V)
Now that you have the perpendicular height, you can use the standard volume formula for a cone:
\(V = \frac{1}{3} \pi r^2 h\)
The video gives a clear, step-by-step approach to find the volume of a cone given its slant height.
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