To find the volume of a cone, we use the formula for the volume of a cone, which is:
[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]
Given:
- The base area of the cone ([tex]\( A \)[/tex]) is [tex]\( 49 \, \text{cm}^2 \)[/tex].
- The height of the cone ([tex]\( h \)[/tex]) is [tex]\( 3 \, \text{cm} \)[/tex].
Now, we substitute the given values into the formula:
[tex]\[ V = \frac{1}{3} \times 49 \, \text{cm}^2 \times 3 \, \text{cm} \][/tex]
First, multiply the base area by the height:
[tex]\[ 49 \times 3 = 147 \][/tex]
Next, multiply the result by [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ \frac{1}{3} \times 147 = 49 \][/tex]
Thus, the volume of the cone is:
[tex]\[ 49 \, \text{cm}^3 \][/tex]
Therefore, the correct answer is:
c) [tex]\( 49 \, \text{cm}^3 \)[/tex]
