Part A
The correct answer is 11 inches. Students will be provided with a reference sheet during the test, so it is not necessary for them to memorize formulas. The formula for the volume, V, of a cone is given by this formula:V equals one third pi R squared H
$$ V=\frac{1}{3}\pi r^2 h $$
where r is the radius of the circular base and h is the height. You are given the volume (414.7 cubic inches) and the radius (6 inches), so you need to find the height, which you can do by plugging the known values into the volume equation and solving for h.414 point 7 is approximately equal to one third times 3.14159 times 6 squared times h
$$ 414.7 \approx \frac{1}{3} \times 3.14159 \times 6^2 \times h $$
In order to get rid of the fraction, multiply both sides of the equation by 3 to simplify, and then isolate h:3 times 414 point 7 is approximately equal to 3 times one-third times 3.14159 times 36 times h
$$ 3 \times 414.7 \approx 3 \times \frac{1}{3} \times 3.14159 \times 36 \times h $$
1 thousand 2 hundred 44 point 1 is approximately equal to 1 hundred 13 point 0 9 7 2 4 times H $$ 1244.1 \approx 113.09724 \times h $$
1 thousand 2 hundred 44 point 1 divided by 113.09724 is approximately equal to H $$ \frac{1244.1}{113.09724} \approx h $$
Doing the division, you find that h is approximately 11 inches.
Part B
1206 cubic inches
Note
Fill-in-the-blank questions, like this one, sometimes allow students to enter commas in their numbers. For example, the answer to Part B (1206) could be entered as "1,206" on some test-delivery platforms. If commas are entered, placing them incorrectly will not affect the score. Only the digits and any decimal points entered are counted when scoring this type of question on the MCAP. In other words, a response of "12,06" would be counted as correct for Part B.