Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

What is the height of a pyramid with a volume of 600 cm³ and a base area of 24 cm²?

Enter the answer in the box:

Height = _____ cm


Sagot :

To find the height of a pyramid given its volume and base area, we can use the formula for the volume of a pyramid:

[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]

Given:
- [tex]\( V = 600 \, \text{cm}^3 \)[/tex]
- [tex]\(\text{base area} = 24 \, \text{cm}^2 \)[/tex]

We need to find the height of the pyramid ([tex]\(h\)[/tex]).

Step 1: Write the formula for the volume of the pyramid.
[tex]\[ 600 = \frac{1}{3} \times 24 \times h \][/tex]

Step 2: Simplify the equation.
[tex]\[ 600 = 8h \][/tex]

Step 3: Solve for [tex]\(h\)[/tex] by dividing both sides of the equation by 8.
[tex]\[ h = \frac{600}{8} \][/tex]

Step 4: Calculate the division.
[tex]\[ h = 75 \][/tex]

So, the height of the pyramid is:
[tex]\[ \boxed{75} \, \text{cm} \][/tex]