David as asked to find the volume of the shape below. Use 3.14 for π.
Identify David's error and show all steps to arrive to the correct answer.
Math
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David's error is that he calculated the volume of a cylinder instead of a cone.
The formula for the volume of a cone is given by:
$$V = \dfrac{1}{3} \times \pi \times r^2 \times h$$
Given that:
Radius (r) = 7 cm
Height (h) = 9 cm
Substitute the values into the formula:
$$V = \dfrac{1}{3} \times 3.14 \times 7^2 \times 9$$
$$V = \dfrac{1}{3} \times 3.14 \times 49 \times 9$$
$$V = \dfrac{1}{3} \times 3.14 \times 441$$
$$V = \dfrac{1}{3} \times 1386.74$$
$$V = 462.25 cm^3$$
So, the correct volume of the cone is 462.25 cm^3.
are you sure
Apologies for the mistake in my previous response. Let's correct that:
For the volume of a cone, the formula is:
\[ V = \dfrac{1}{3} \pi r^2 h \]
Given:
- Radius (\( r \)) = 7 cm
- Height (\( h \)) = 9 cm
- \( \pi = 3.14 \)
Substitute the values into the formula:
\[ V = \dfrac{1}{3} \times 3.14 \times 7^2 \times 9 \]
\[ V = \dfrac{1}{3} \times 3.14 \times 49 \times 9 \]
\[ V = \dfrac{1}{3} \times 3.14 \times 441 \]
\[ V = \dfrac{1}{3} \times 1386.54 \]
\[ V = 462.54 \text{ cm}^3\]
Therefore, the correct volume of the cone is 462.54 cm^3. Thank you for pointing out the error.