Math Problem Statement

What is the approximate volume of the cone? Use 3.14 for π.

Solution

To solve for the approximate volume of the cone shown in the image, we use the formula for the volume of a cone:

V=13πr2hV = \frac{1}{3} \pi r^2 h

Step 1: Identify the given values

  • Radius of the base of the cone (rr): 5cm5 \, \text{cm} (from the image)
  • Height of the cone (hh): 6cm6 \, \text{cm}
  • Approximation for π\pi: 3.143.14

Step 2: Plug in the values

V=133.14(5)26V = \frac{1}{3} \cdot 3.14 \cdot (5)^2 \cdot 6

Step 3: Simplify the calculations

  1. Compute r2r^2: 52=255^2 = 25

  2. Multiply by hh: 256=15025 \cdot 6 = 150

  3. Multiply by π\pi: 1503.14=471150 \cdot 3.14 = 471

  4. Divide by 3: 4713=157\frac{471}{3} = 157

Final Answer:

The approximate volume of the cone is: 157cm3\boxed{157 \, \text{cm}^3}

Do you want further clarifications or detailed steps? Let me know!


Here are 5 related questions to explore further:

  1. How is the formula for the volume of a cone derived?
  2. What is the difference between the volume and surface area of a cone?
  3. How would the volume change if the height doubled but the radius stayed the same?
  4. How does the approximation of π\pi affect the accuracy of the volume calculation?
  5. Can you find the volume of a cone if only the slant height and radius are given?

Tip: Always double-check your units when solving geometry problems to ensure accuracy!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Volume of 3D Shapes
Cone Volume Calculation

Formulas

Volume of a cone: V = (1/3)πr²h

Theorems

-

Suitable Grade Level

Grades 6-8