SOLUTION: The top of a cone of height 10cm and base radius 7cm is cut off by a plane parallel to the base. If the distance between the plane and the base is 3cm, calculate the volume of the

Question 1209538: The top of a cone of height 10cm and base radius 7cm is cut off by a plane parallel to the base. If the distance between the plane and the base is 3cm, calculate the volume of the remaining object. [Take π = 22/7]
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source): You can put this solution on YOUR website!
Here's how to calculate the volume of the remaining object (which is a frustum):
**1. Find the radius of the top of the frustum:**
* The original cone has a height of 10 cm and a radius of 7 cm.
* The top of the cone is cut off 3 cm from the base, leaving a smaller cone with a height of 10 - 3 = 7 cm.
* The ratio of the radius to the height in similar triangles is constant. So, the radius of the top of the frustum (r) can be found using the proportion:
r / 7 = 7 / 10
r = (7 * 7) / 10
r = 4.9 cm
**2. Calculate the volume of the frustum:**
The formula for the volume of a frustum is:
V = (1/3) * π * h * (R² + r² + Rr)
Where:
* V is the volume of the frustum
* π is approximately 22/7
* h is the height of the frustum (3 cm)
* R is the radius of the base (7 cm)
* r is the radius of the top (4.9 cm)
Plugging in the values:
V = (1/3) * (22/7) * 3 * (7² + 4.9² + 7 * 4.9)
V = (22/7) * (49 + 24.01 + 34.3)
V = (22/7) * 107.31
V ≈ 337.26 cm³
Therefore, the volume of the remaining object (the frustum) is approximately $\boxed{337.26}$ cm³.

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
The top of a cone of height 10cm and base radius 7cm is cut off by a plane parallel to the base.
If the distance between the plane and the base is 3cm, calculate the volume of the remaining object. [Take π = 22/7]
~~~~~~~~~~~~~~~~~~~~~~~~~

            Here is another, more simple, more straightforward
            and computationally less extensive solving method.

The volume of the original cone is V = = = 513.33333 cm^3. The smaller cone is similar to the original one with the similarity coefficient = = 0.7. Therefore, the volume of the smaller cone is = = 176.07533 cm^3. The volume of the interest is the difference 513.33333 - 176.07533 = 337.26 cm^3. ANSWER<. The volume of the remaining object is 337.26 cm^3 (approximately).

Solved in different way.

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