Question
A cone-shaped play tent has a radius of 4 feet and a slant height of 7 feet. If Joe is six feet tall, which of the following statements is true?
U9Q7TestQuestion-1.jpg
Joe is taller than the tent.
Joe is shorter than the tent.
Joe is the same height as the tent.
There is not enough information to determine if Joe is shorter or taller than the tent.A cone-shaped play tent has a radius of 4 feet and a slant height of 7 feet. If Joe is six feet tall, which of the following statements is true?
U9Q7TestQuestion-1.jpg
Joe is taller than the tent.
Joe is shorter than the tent.
Joe is the same height as the tent.
There is not enough information to determine if Joe is shorter or taller than the tent.
U9Q7TestQuestion-1.jpg
Joe is taller than the tent.
Joe is shorter than the tent.
Joe is the same height as the tent.
There is not enough information to determine if Joe is shorter or taller than the tent.A cone-shaped play tent has a radius of 4 feet and a slant height of 7 feet. If Joe is six feet tall, which of the following statements is true?
U9Q7TestQuestion-1.jpg
Joe is taller than the tent.
Joe is shorter than the tent.
Joe is the same height as the tent.
There is not enough information to determine if Joe is shorter or taller than the tent.
Answers
Answered by
GPT-4o mini
To determine how tall the cone-shaped play tent is, we can use the slant height and the radius to find the vertical height (h) of the cone using the Pythagorean theorem.
Given:
- Radius (r) = 4 feet
- Slant height (l) = 7 feet
The relationship between the radius, height, and slant height in a right triangle is:
\[ l^2 = r^2 + h^2 \]
We can rearrange this to find the height \( h \):
\[ h^2 = l^2 - r^2 \]
Now, substituting the values:
\[ h^2 = 7^2 - 4^2 \]
\[ h^2 = 49 - 16 \]
\[ h^2 = 33 \]
\[ h = \sqrt{33} \]
Calculating \( \sqrt{33} \):
\[ h \approx 5.74 \text{ feet} \]
Now, comparing Joe's height (6 feet) to the height of the tent (approximately 5.74 feet):
Joe is 6 feet tall, which is taller than the height of the tent (approximately 5.74 feet).
Therefore, the correct statement is:
**Joe is taller than the tent.**
Given:
- Radius (r) = 4 feet
- Slant height (l) = 7 feet
The relationship between the radius, height, and slant height in a right triangle is:
\[ l^2 = r^2 + h^2 \]
We can rearrange this to find the height \( h \):
\[ h^2 = l^2 - r^2 \]
Now, substituting the values:
\[ h^2 = 7^2 - 4^2 \]
\[ h^2 = 49 - 16 \]
\[ h^2 = 33 \]
\[ h = \sqrt{33} \]
Calculating \( \sqrt{33} \):
\[ h \approx 5.74 \text{ feet} \]
Now, comparing Joe's height (6 feet) to the height of the tent (approximately 5.74 feet):
Joe is 6 feet tall, which is taller than the height of the tent (approximately 5.74 feet).
Therefore, the correct statement is:
**Joe is taller than the tent.**