Question

a construction company is putting cone - shaped tops on top of each bridge support to discourage birds from roosting on the bridge. each cone will be filled with cement. how much cement will they have to put in each cone? (use π = 3.14.)
a) 942 cm³
b) 271.2 cm³
c) 314 cm³
d) 282.6 cm³
question 9 (5 points)

Explanation:

Step1: Recall the volume formula for a cone

The volume \( V \) of a cone is given by the formula \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius of the base and \( h \) is the height of the cone.

Step2: Identify the values of \( r \) and \( h \)

From the diagram, the radius \( r = 5\space\text{cm}\) and the height \( h=12\space\text{cm}\), and \( \pi = 3.14\).

Step3: Substitute the values into the formula

First, calculate \( r^{2}\): \( r^{2}=5^{2} = 25\).
Then, calculate \( \pi r^{2}h\): \( 3.14\times25\times 12=3.14\times300 = 942\).
Finally, calculate \( \frac{1}{3}\pi r^{2}h\): \( \frac{1}{3}\times942 = 314\)? Wait, no, wait, let's recalculate. Wait, \( \frac{1}{3}\times3.14\times25\times12\). Let's compute \( 25\times12 = 300\), then \( \frac{1}{3}\times300=100\), then \( 3.14\times100 = 314\)? Wait, no, wait the options have 282.6? Wait, maybe I made a mistake. Wait, no, let's check again. Wait, \( \frac{1}{3}\times3.14\times5^{2}\times12\). \( 5^{2}=25\), \( 25\times12 = 300\), \( \frac{1}{3}\times300 = 100\), \( 3.14\times100=314\)? But option D is 282.6. Wait, maybe the radius is 5, height is 12. Wait, no, maybe I misread the diagram. Wait, no, the formula is \( \frac{1}{3}\pi r^{2}h\). Let's compute again: \( \frac{1}{3}\times3.14\times5^{2}\times12=\frac{1}{3}\times3.14\times25\times12\). \( 25\times12 = 300\), \( \frac{1}{3}\times300 = 100\), \( 3.14\times100 = 314\)? But the options: A) 942, B)271.2, C)314, D)282.6. Wait, maybe the height is different? Wait, no, the diagram shows height 12, radius 5. Wait, maybe I made a mistake in the formula? No, the volume of a cone is \( \frac{1}{3}\pi r^{2}h \). Wait, let's compute \( \frac{1}{3}\times3.14\times5^{2}\times12\):

\( 5^{2}=25 \)

\( 25\times12 = 300 \)

\( \frac{1}{3}\times300 = 100 \)

\( 3.14\times100 = 314 \). But option C is 314. Wait, but let's check the options again. Wait, maybe the height is 9? No, the diagram says 12. Wait, maybe the radius is 4? No, the diagram says 5. Wait, maybe I made a mistake. Wait, no, let's check the calculation again. \( \frac{1}{3}\times3.14\times5^{2}\times12\). Let's compute step by step:

\( 5^{2}=25 \)

\( 25\times12 = 300 \)

\( 3.14\times300 = 942 \)

\( \frac{1}{3}\times942 = 314 \). Yes, so the volume is \( 314\space\text{cm}^3 \). Wait, but option D is 282.6. Wait, maybe the radius is 5 and height is 9? No, the diagram shows 12. Wait, maybe the problem has a typo, but according to the given values, the calculation is \( \frac{1}{3}\times3.14\times5^{2}\times12 = 314 \). So the answer should be C) 314 \( \text{cm}^3 \). Wait, but let's check again. Wait, \( \frac{1}{3}\times3.14\times5^2\times12=\frac{1}{3}\times3.14\times25\times12 = 3.14\times25\times4=3.14\times100 = 314 \). Yes, that's correct.

Answer:

C) 314 \( \text{cm}^3 \)