Question

a local high schools cheerleading squad is selling snow cones during lunch to raise money for a national cheerleading competition.Paper cones are pre-filled with shaved ice and then filled with flavored syrup as customers orders are placed.The paper can contain no more than 535 cubic centimeters of shaved ice and syrup.If the paper cone is 8 centimeters deep,what is the largest width of the containers opening?Use 3.14 to approximate pi.Round your answer to the nearest whole unit.

Answer 1

We have:

Volume of cone = 535 cm³ at the maximum
Height of cone= 8cm

We know the formula to find volume of cone is $\frac{1}{3} r^{2} \pi h$

We need to find the radius of the base of the cone
$535= \frac{\pi r^{2}8} {3}$
$535*8= \pi r^{2}$
$\frac{4280}{\pi}= r^{2}$
$r= \sqrt{ \frac{4280}{ \pi} }$
$r=36.9$ to the nearest one decimal place

The width of the opening of the cone is the diameter of the circle. Diameter is twice the radius, hence 2×36.9=73.8 cm