Math Problem Statement

Find the volume of the figure when b = 4 ft and h = 6 ft.

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Find the volume of the figure when b = 4 ft and h = 6 ft.

Solution

The image depicts a square pyramid, with the base having side length bb and height hh.

The formula to find the volume VV of a pyramid is:

V=13×Base Area×HeightV = \frac{1}{3} \times \text{Base Area} \times \text{Height}

For a square base, the base area AA is given by:

A=b2A = b^2

Substituting into the volume formula:

V=13×b2×hV = \frac{1}{3} \times b^2 \times h

Given b=4ftb = 4 \, \text{ft} and h=6fth = 6 \, \text{ft}:

V=13×42×6=13×16×6=13×96=32ft3V = \frac{1}{3} \times 4^2 \times 6 = \frac{1}{3} \times 16 \times 6 = \frac{1}{3} \times 96 = 32 \, \text{ft}^3

Thus, the volume of the pyramid is 32 cubic feet.

Would you like more details or have any other questions?

Here are some follow-up questions to deepen understanding:

  1. How does the volume formula change for other types of pyramids?
  2. What would happen to the volume if the height doubled but the base stayed the same?
  3. How is the formula for a cone's volume similar to that of a pyramid?
  4. What is the significance of the 13\frac{1}{3} factor in the volume formula?
  5. How would you calculate the surface area of this pyramid?

Tip: When dealing with pyramids, always verify the base shape and dimensions before applying the volume formula.

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Math Problem Analysis

Mathematical Concepts

Geometry
Solid Figures
Pyramids

Formulas

Volume of a Pyramid: V = (1/3) * Base Area * Height
Base Area for Square Pyramid: A = b^2

Theorems

Volume theorem for pyramids and cones

Suitable Grade Level

Grades 6-9