To determine which statement is true, we calculate the height of the cone-shaped tent. The height $h$ of the cone can be found using the Pythagorean theorem, as the radius ($r$), height ($h$), and slant height ($l$) of the cone form a right triangle:

$l^2 = r^2 + h^2$

Given:

• Radius ($r$) = 4 feet
• Slant height ($l$) = 7 feet

Calculation:

$7^2 = 4^2 + h^2$ $49 = 16 + h^2$ $h^2 = 49 - 16 = 33$ $h = \sqrt{33} \approx 5.74 \, \text{feet}$

Comparison:

• Joe is 6 feet tall.
• The height of the tent is approximately 5.74 feet.

Since Joe's height ($6$ feet) is greater than the height of the tent ($5.74$ feet):

Joe is taller than the tent.

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Would you like further details or a breakdown of the Pythagorean theorem?

Relative Questions:

1. How is the slant height related to the radius and height in a cone?
2. What are some real-life examples where the Pythagorean theorem is applied?
3. How can you calculate the surface area of a cone with the given dimensions?
4. What is the volume of this cone-shaped tent?
5. How would the height change if the radius was doubled?

Tip:

Always verify whether the given slant height is for the cone or a separate measurement to avoid confusion.