Question

Sarah is making paper cones to serve nuts for a party at school. The volume of each cone is 78 cubic centimeters, and the height is
9 cm. She wants to store the cones side by side in rows in a container in the shape of a rectangular prism, with a length of 50 cm, a
width of 24 cm, and a height of 9 cm.
Complete the statements below, rounding to the nearest hundredth if necessary. Use 3.14 for pi.
The diameter of each paper cone is about ____cm.
Sarah can fit a maximum of ___paper cones in the container.

Answer 1

Answer:

Part 1) The diameter of each cone paper is about 5.76 cm

Part 2) 32 paper cones

Step-by-step explanation:

step 1

Find the diameter of each paper cone

we know that

The volume of a cone is given by the formula

$V=\frac{1}{3}\pi r^{2} h$

we have

$V=78\ cm^3\\h=9\ cm$

assume

$\pi =3.14$

substitute

$78=\frac{1}{3}(3.14)r^{2}(9)$

solve for r

$78=9.42r^{2}$

$r=2.88\ cm$

Find the diameter

Remember that the diameter is two times the radius

so

$D=2(2.88)=5.76\ cm$

step 2

Find out the maximum number of paper cone that Sarah can fit in the prism

by the height of the prim can fit 1 (divide the height of the prism by the height of the cone)

by the width of the prism can fit 24/5.76=4 (Divide the width of the prism by the diameter of the cone and round down)

by the length of the prism can fit 50/5.76=8 (Divide the length of the prism by the diameter of the cone and round down)

so

The maximum number of paper cone is equal t

$(1)(4)(8)=32\ paper\ cones$