Question

a) select the appropriate formula to determine volume of a cone. bh 1/3 πr²h 4/3 πr³ πr²h lwh 1/3 bh part 2 of 3 b) identify the variables. r = 9 ft 9 = 9 h = 27 un 27 = 27 part 3 of 3 c) calculate the volume. v = 1/3 πr²h v = ft³ question help: video

Explanation:

Step1: Recall the cone volume formula

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

Step2: Substitute the given values

We know that \( r = 9 \) ft and \( H = 27 \) ft. Substitute these values into the formula:
\( V=\frac{1}{3}\pi(9)^{2}(27) \)

Step3: Calculate the numerical part

First, calculate \( 9^{2}=81 \). Then, multiply \( \frac{1}{3}\times81\times27 \).
\( \frac{1}{3}\times81 = 27 \), and \( 27\times27 = 729 \). So, \( V = 729\pi \) (or if we use \( \pi\approx3.14 \), \( V\approx729\times3.14 = 2290.2 \))

Answer:

If using \( \pi \) as a symbol, the volume is \( 729\pi \) cubic feet. If using \( \pi\approx3.14 \), the volume is approximately \( 2290.2 \) cubic feet. (Commonly, if we need a numerical value with \( \pi\approx3.14 \), the answer is \( 2290.2 \); if leaving \( \pi \) in the expression, it's \( 729\pi \).)