Math Problem Statement

The volume of the rectangular-based pyramid below is 544 cm³. What is the perpendicular height of this pyramid? Give your answer in centimetres (cm), and give any decimal answers to 1 d.p.

Solution

To solve the problem:

Step 1: Formula for the volume of a pyramid

The formula for the volume of a pyramid is:

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

Step 2: Find the base area

The base of the pyramid is a rectangle with dimensions 12 cm × 8 cm. The base area is:

Base Area=12×8=96cm2\text{Base Area} = 12 \times 8 = 96 \, \text{cm}^2

Step 3: Substitute the given volume

The volume of the pyramid is 544 cm³. Substitute into the formula:

544=13×96×h544 = \frac{1}{3} \times 96 \times h

Step 4: Solve for height hh

Rearrange the formula to solve for hh:

h=544×396h = \frac{544 \times 3}{96}

Simplify:

h=163296=17cmh = \frac{1632}{96} = 17 \, \text{cm}

Final Answer:

The perpendicular height of the pyramid is:

17cm\boxed{17 \, \text{cm}}

Would you like additional clarification or more details on the calculation steps?


Here are 5 related questions to consider:

  1. How do you calculate the volume of a triangular-based pyramid?
  2. What happens to the volume if the height doubles?
  3. How can you find the height if the base is irregularly shaped?
  4. Why is the 13\frac{1}{3} factor used in the pyramid volume formula?
  5. How would this problem change if the base was a triangle instead of a rectangle?

Tip: Always double-check your unit conversions to ensure accuracy when solving geometric problems!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Volume of a Pyramid
Rectangular Base

Formulas

Volume of a Pyramid: V = (1/3) × Base Area × Height

Theorems

-

Suitable Grade Level

Grades 7-10