https://file.aiquickdraw.com/mathbot/file/1726408394313w7qtb7pj.jpg

To solve the problem, we need to calculate the volume of a triangular pyramid (S.LPT) where:

- The base \( LPT \) is an equilateral triangle with side length \( 66 \, \text{mm} \).
- The height of the pyramid \( SO = 48 \, \text{mm} \).
- \( O \) is the centroid of the base triangle \( LPT \).
- The height of triangle \( LPT \) is \( OH = 11\sqrt{3} \, \text{mm} \).

### Formula for the Volume of a Pyramid:
The volume \( V \) of a pyramid is given by the formula:
\[
V = \frac{1}{3} \times A_{\text{base}} \times h
\]
Where:
- \( A_{\text{base}} \) is the area of the base (triangle \( LPT \)).
- \( h = SO = 48 \, \text{mm} \) is the height of the pyramid from \( S \) to the base \( LPT \).

### Step 1: Calculate the Area of Triangle \( LPT \)
The area of an equilateral triangle is:
\[
A_{\text{base}} = \frac{s^2 \sqrt{3}}{4}
\]
Where \( s = 66 \, \text{mm} \).

### Step 2: Use the Pyramid Volume Formula
Substitute \( A_{\text{base}} \) and \( h \) into the volume formula to get the result.

I will now calculate the solution.The volume of the triangular pyramid \( S.LPT \) is approximately \( 30179.3 \, \text{mm}^3 \).

Do you need further clarification or details on any of the steps? 

Here are some related questions you might consider:

1. How is the centroid of a triangle calculated?
2. What are other methods for calculating the volume of pyramids?
3. How does the area of an equilateral triangle relate to its side length?
4. What is the significance of \( OH = 11\sqrt{3} \, \text{mm} \) in this problem?
5. How would the volume change if the height of the pyramid doubled?

**Tip:** When working with three-dimensional objects, always confirm if the base area and the height are perpendicular for accurate volume calculation.

Tính thể tích của hình chóp tam giác đều S.LPT biết cạnh đáy bằng 66mm, chiều cao của hình chóp SO = 48mm, O là trọng tâm tam giác đáy LPT, TH là đường cao của tam giác LPT; OH = 11√3 mm. (Làm tròn các kết quả đến hàng phần mười)

Learn how to calculate the volume of a triangular pyramid (S.LPT) where the base is an equilateral triangle with a side length of 66mm and a height of 48mm. The centroid and the height from the centroid to the base are provided. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation