Answer :
To find the volume of a cone, you can use the formula:
[tex]\[ \text{Volume} = \frac{1}{3} \pi r^2 h \][/tex]
where:
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone,
- \( \pi \) is a constant approximately equal to 3.14159.
Given:
- The height \( h \) is 3 cm.
- The base radius \( r \) is 7 cm.
Now, substitute the values of \( h \) and \( r \) into the formula:
[tex]\[ \text{Volume} = \frac{1}{3} \pi (7 \, \text{cm})^2 (3 \, \text{cm}) \][/tex]
First, calculate the radius squared:
[tex]\[ 7^2 = 49 \][/tex]
Next, multiply this by the height:
[tex]\[ 49 \times 3 = 147 \][/tex]
Now, include the constant \(\pi\) and the factor \(\frac{1}{3}\):
[tex]\[ \text{Volume} = \frac{1}{3} \pi \times 147 \][/tex]
[tex]\[ \text{Volume} = \frac{147}{3} \times \pi \][/tex]
[tex]\[ \text{Volume} = 49 \times \pi \][/tex]
Finally, when you multiply 49 by \(\pi\) (approximately 3.14159), you get:
[tex]\[ 49 \times 3.14159 \approx 153.94 \][/tex]
So, the volume of the cone is approximately \( 153.94 \, \text{cm}^3 \).
Therefore, the closest answer from the options given is:
B. 154 cm³
[tex]\[ \text{Volume} = \frac{1}{3} \pi r^2 h \][/tex]
where:
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone,
- \( \pi \) is a constant approximately equal to 3.14159.
Given:
- The height \( h \) is 3 cm.
- The base radius \( r \) is 7 cm.
Now, substitute the values of \( h \) and \( r \) into the formula:
[tex]\[ \text{Volume} = \frac{1}{3} \pi (7 \, \text{cm})^2 (3 \, \text{cm}) \][/tex]
First, calculate the radius squared:
[tex]\[ 7^2 = 49 \][/tex]
Next, multiply this by the height:
[tex]\[ 49 \times 3 = 147 \][/tex]
Now, include the constant \(\pi\) and the factor \(\frac{1}{3}\):
[tex]\[ \text{Volume} = \frac{1}{3} \pi \times 147 \][/tex]
[tex]\[ \text{Volume} = \frac{147}{3} \times \pi \][/tex]
[tex]\[ \text{Volume} = 49 \times \pi \][/tex]
Finally, when you multiply 49 by \(\pi\) (approximately 3.14159), you get:
[tex]\[ 49 \times 3.14159 \approx 153.94 \][/tex]
So, the volume of the cone is approximately \( 153.94 \, \text{cm}^3 \).
Therefore, the closest answer from the options given is:
B. 154 cm³
