Math Problem Statement

What is the volume of this cone?

Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth. Height is 5 radius is 4.4

Solution

To find the volume of a cone, we can use the formula:

V=13πr2hV = \frac{1}{3} \pi r^2 h

Where:

  • π3.14\pi \approx 3.14
  • rr is the radius of the base
  • hh is the height of the cone

Given:

  • r=4.4r = 4.4
  • h=5h = 5

Now, substitute the values into the formula:

V=13×3.14×(4.4)2×5V = \frac{1}{3} \times 3.14 \times (4.4)^2 \times 5

First, calculate the square of the radius:

4.42=19.364.4^2 = 19.36

Now, calculate the volume:

V=13×3.14×19.36×5V = \frac{1}{3} \times 3.14 \times 19.36 \times 5

V=13×3.14×96.8V = \frac{1}{3} \times 3.14 \times 96.8

V=13×303.472V = \frac{1}{3} \times 303.472

V101.16V \approx 101.16

So, the volume of the cone is approximately 101.16 cubic units.

Would you like more details on how I solved this, or do you have any questions?

Here are 5 related questions:

  1. How do you find the surface area of a cone?
  2. What is the formula to calculate the volume of a cylinder?
  3. How would the volume change if the height was doubled?
  4. What is the effect of increasing the radius on the volume of a cone?
  5. Can you calculate the volume if the cone had a different value for pi, like 3.1416?

Tip: Always square the radius before multiplying with other values in the volume formula!

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume of a Cone
Pi Approximation

Formulas

V = (1/3) * π * r^2 * h

Theorems

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Suitable Grade Level

Grades 6-8