Question
A chemist has filled a funnel with a compound and needs to know how deep the funnel is. The radius and slant height are measured as shown. If the depth, radius, and slant height form a right triangle, how deep is the funnel? Round to the nearest whole number, if needed. (1 point) Responses The funnel is 15 cm deep. The funnel is 15 cm deep. The funnel is 18 cm deep. The funnel is 18 cm deep. The funnel is 12 cm deep. The funnel is 12 cm deep. The funnel is 5 cm deep. The funnel is 5 cm deep.
Answers
GPT-4o mini
To determine the depth of the funnel, we can use the Pythagorean theorem since the depth (h), radius (r), and slant height (l) form a right triangle. The equation is given by:
\[
l^2 = r^2 + h^2
\]
Given the options provided, we would need the specific measurements for the radius and the slant height to calculate the depth. However, if we assume hypothetical values (that are consistent with common funnel dimensions), we can calculate it accordingly.
Let's say:
- Radius (r) = 12 cm
- Slant height (l) = 18 cm
We can use the Pythagorean theorem to solve for depth (h):
1. Calculate \(h\):
\[
18^2 = 12^2 + h^2
\]
\[
324 = 144 + h^2
\]
2. Rearranging gives:
\[
h^2 = 324 - 144
\]
\[
h^2 = 180
\]
3. Taking the square root:
\[
h = \sqrt{180} \approx 13.42 \text{ cm}
\]
Rounding to the nearest whole number gives us **13 cm**.
However, you should repeat these calculations with the radius and slant height values you have measured, and substitute them into the Pythagorean theorem formula as shown above to find the corresponding depth.
From your options:
- The funnel is 15 cm deep.
- The funnel is 18 cm deep.
- The funnel is 12 cm deep.
- The funnel is 5 cm deep.
The answer would depend on the actual numerical values provided for the radius and slant height. If any of these choices came from calculations based on valid r and l values, you would select that option based on your calculations. Please provide the measurements for a precise answer.
\[
l^2 = r^2 + h^2
\]
Given the options provided, we would need the specific measurements for the radius and the slant height to calculate the depth. However, if we assume hypothetical values (that are consistent with common funnel dimensions), we can calculate it accordingly.
Let's say:
- Radius (r) = 12 cm
- Slant height (l) = 18 cm
We can use the Pythagorean theorem to solve for depth (h):
1. Calculate \(h\):
\[
18^2 = 12^2 + h^2
\]
\[
324 = 144 + h^2
\]
2. Rearranging gives:
\[
h^2 = 324 - 144
\]
\[
h^2 = 180
\]
3. Taking the square root:
\[
h = \sqrt{180} \approx 13.42 \text{ cm}
\]
Rounding to the nearest whole number gives us **13 cm**.
However, you should repeat these calculations with the radius and slant height values you have measured, and substitute them into the Pythagorean theorem formula as shown above to find the corresponding depth.
From your options:
- The funnel is 15 cm deep.
- The funnel is 18 cm deep.
- The funnel is 12 cm deep.
- The funnel is 5 cm deep.
The answer would depend on the actual numerical values provided for the radius and slant height. If any of these choices came from calculations based on valid r and l values, you would select that option based on your calculations. Please provide the measurements for a precise answer.