Question
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
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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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!