Question

a chef pours 550 cubic centimeters of batter into a baking pan in the shape of a right circular cylinder. if the pan has a radius of 6 cm, how high does the batter fill the baking pan? round your answer to the nearest tenth of a centimeter. use 3.14 for π. 4.9 cm 29.2 cm 8.6 cm 15.3 cm

Explanation:

Step1: Recall the volume formula for a cylinder

The volume \( V \) of a right circular cylinder is given by the formula \( V=\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height. We know \( V = 550\space cm^{3}\), \( r=6\space cm \) and \( \pi = 3.14 \). We need to solve for \( h \). Rearranging the formula for \( h \), we get \( h=\frac{V}{\pi r^{2}} \).

Step2: Calculate the area of the base (\( \pi r^{2} \))

Substitute \( r = 6 \) and \( \pi=3.14 \) into \( \pi r^{2} \). So \( \pi r^{2}=3.14\times6^{2}=3.14\times36 = 113.04\space cm^{2} \).

Step3: Calculate the height \( h \)

Substitute \( V = 550 \) and \( \pi r^{2}=113.04 \) into the formula for \( h \). So \( h=\frac{550}{113.04}\approx4.9\space cm \) (rounded to the nearest tenth).

Answer:

4.9 cm