Question - Calculating Volume of a Cone
Solution:
The question in the image is asking for the volume of a cone. The formula to calculate the volume of a cone is:\[ \text{Volume} = \frac{1}{3} \pi r^2 h \]where $$ \pi $$ is Pi, approximately 3.14159, $$ r $$ is the radius of the base of the cone, and $$ h $$ is the height of the cone.According to the image, the ice cream cone has a diameter of 3 inches, which means the radius $$ r $$ is half of that, so $$ r = 1.5 $$ inches. The height $$ h $$ of the cone is given as 7 inches.Now plug these values into the formula to find the volume:\[ \text{Volume} = \frac{1}{3} \pi (1.5)^2 \cdot 7 \]\[ \text{Volume} = \frac{1}{3} \pi \cdot 2.25 \cdot 7 \]\[ \text{Volume} = \frac{1}{3} \cdot 3.14159 \cdot 2.25 \cdot 7 \]\[ \text{Volume} = \frac{1}{3} \cdot 3.14159 \cdot 15.75 \]\[ \text{Volume} = 3.14159 \cdot 5.25 \]\[ \text{Volume} = 16.49351 \cdot 3 \]\[ \text{Volume} = 49.480525 \text{ in}^3 \]Rounded to the nearest tenth, the volume is approximately 49.5 cubic inches.Based on the answer choices provided in the image, none of them match this exact answer. It might be a good idea to double-check the calculations or see if the image contains any error in the question or answer options.
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