Question
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A metal sheet with volump is melted and recast into sma let cones of cqual si
Ench cone has base circumference of 12 cm and slant height of 5 cm .
The volume of the cone of radlus r and helght h is .
(a) Calculate the volume of the cone

Ask by Bowman Stuart. in Lesotho
Jan 16,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The volume of each cone is approximately 17.7 cm³.

Solution

To calculate the volume of each cone, let’s follow these steps:

Given:

  • Volume of metal sheet: (this is used for determining the number of cones, not directly needed for part (a)).
  • Base circumference of the cone:
  • Slant height of the cone:
  • Volume formula for a cone:

Step 1: Find the Radius ( ) of the Cone

The circumference of the base is related to the radius by the formula:
Solving for :

Step 2: Find the Height ( ) of the Cone

Using the Pythagorean theorem for the right triangle formed by the radius, height, and slant height:
Solving for :

Step 3: Calculate the Volume ( ) of the Cone

Now, plug the values of and into the volume formula:
Simplifying:

Final Answer:

The volume of each cone is approximately 17.7 cm³.

Answered by UpStudy AI and reviewed by a Professional Tutor

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Simplify this solution

The Deep Dive

To calculate the volume of the cone, we start with the relationship between the circumference and the radius. The circumference of the cone’s base is given by:
Given that , we can solve for :
Next, we need to find the height using the Pythagorean theorem, as we have the slant height :
Calculating :
Now we find :
Finally, we can find the volume :
Substituting the values of and gives the volume of one cone. Plug in the calculated values to find the exact volume.
Final Formula:
Simplify to get the numerical answer!

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