Volume of a Triangular Pyramid Worksheets - Free Printable

I'll solve the problems on this worksheet about finding the volume of triangular pyramids. Let me go through each problem one by one.

Problem 1: Volume = 500 ft³

Looking at the first pyramid, I can see:
- Base is a right triangle with legs of 10 ft and 12 ft
- Height of the pyramid is labeled as "h"
- Volume is given as 500 ft³

The formula for the volume of a pyramid is: V = (1/3) × B × h, where B is the area of the base.

First, calculate the area of the triangular base:
B = (1/2) × 10 ft × 12 ft = 60 ft²

Now use the volume formula:
500 = (1/3) × 60 × h
500 = 20h
h = 500/20 = 25 ft

Answer for Problem 1: h = 25 ft

Problem 2: Volume = 1,800 ft³

Looking at the second pyramid:
- Base is a right triangle with legs of 15 ft and 12 ft
- Height of the pyramid is labeled as "h"
- Volume is given as 1,800 ft³

Calculate the area of the triangular base:
B = (1/2) × 15 ft × 12 ft = 90 ft²

Use the volume formula:
1,800 = (1/3) × 90 × h
1,800 = 30h
h = 1,800/30 = 60 ft

Answer for Problem 2: h = 60 ft

Problem 3: Volume = 70 ft³

Looking at the third pyramid:
- Base is a right triangle with legs of 4 ft and 7 ft
- Height of the pyramid is labeled as "h"
- Volume is given as 70 ft³

Calculate the area of the triangular base:
B = (1/2) × 4 ft × 7 ft = 14 ft²

Use the volume formula:
70 = (1/3) × 14 × h
70 = (14/3)h
h = 70 × 3/14 = 15 ft

Answer for Problem 3: h = 15 ft

Problem 4: Volume = 1,200 ft³

Looking at the fourth pyramid:
- Base is a right triangle with legs of 10 ft and 12 ft
- Height of the pyramid is labeled as "h"
- Volume is given as 1,200 ft³

Calculate the area of the triangular base:
B = (1/2) × 10 ft × 12 ft = 60 ft²

Use the volume formula:
1,200 = (1/3) × 60 × h
1,200 = 20h
h = 1,200/20 = 60 ft

Answer for Problem 4: h = 60 ft

Problem 5: Volume = 44 ft³

Looking at the fifth pyramid:
- Base is a right triangle with legs of 4 ft and 6 ft
- Height of the pyramid is labeled as "h"
- Volume is given as 44 ft³

Calculate the area of the triangular base:
B = (1/2) × 4 ft × 6 ft = 12 ft²

Use the volume formula:
44 = (1/3) × 12 × h
44 = 4h
h = 44/4 = 11 ft

Answer for Problem 5: h = 11 ft

Problem 6: Volume = 182 ft³

Looking at the sixth pyramid:
- Base is a right triangle with legs of 7 ft and 8 ft
- Height of the pyramid is labeled as "h"
- Volume is given as 182 ft³

Calculate the area of the triangular base:
B = (1/2) × 7 ft × 8 ft = 28 ft²

Use the volume formula:
182 = (1/3) × 28 × h
182 = (28/3)h
h = 182 × 3/28 = 19.5 ft

Answer for Problem 6: h = 19.5 ft

Problem 7

This is a word problem: "The base of a pyramid is a triangle with a base and height of 24 inches each. Find the height of the pyramid if its volume is 2,304 cubic inches."

First, calculate the area of the triangular base:
B = (1/2) × 24 in × 24 in = 288 in²

Use the volume formula:
2,304 = (1/3) × 288 × h
2,304 = 96h
h = 2,304/96 = 24 in

Answer for Problem 7: The height of the pyramid is 24 inches.

Problem 8

This is another word problem: "The height of a triangular pyramid is 10 yards and the volume is 120 cubic yards. If the height of the base triangle of the pyramid is 6 yards, determine the base."

We need to find the base length of the triangular base.

We know:
- Volume = 120 yd³
- Height of pyramid = 10 yd
- Height of base triangle = 6 yd
- We need to find the base length of the triangular base (let's call it "b")

First, use the volume formula to find the area of the base:
V = (1/3) × B × h
120 = (1/3) × B × 10
120 = (10/3) × B
B = 120 × 3/10 = 36 yd²

Now we know the area of the triangular base is 36 yd², and we know the height of that triangle is 6 yd.
Using the formula for the area of a triangle: B = (1/2) × base × height
36 = (1/2) × b × 6
36 = 3b
b = 36/3 = 12 yd

Answer for Problem 8: The base of the triangular base is 12 yards.

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## Final Answers:

1. h = 25 ft
2. h = 60 ft
3. h = 15 ft
4. h = 60 ft
5. h = 11 ft
6. h = 19.5 ft
7. The height of the pyramid is 24 inches.
8. The base of the triangular base is 12 yards.