Question

NAMEDATEPERIOD21. Clare has a 1/2 liter bottle full of water. A cone-shaped paper cup has diameter 10 cmand slant height 13 cm as shown. Can she pour all the water into one paper cup, or willit overflow? Explain your reasoning. (3 pts.)(The volume of a cone ismerhand liter = 500 cubic centimeters)10cm13 cm

Answer 1

We have the following:

The first thing is to calculate the volume of the cone

`\begin{gathered} V=(1)/(3)\cdot\pi\cdot r^2\cdot h \\ \end{gathered}`

where r is the radius and h is the height

the radius is half the diameter, like this

`r=(d)/(2)=(10)/(2)=5`

The radius is 5 cm.

Now, for the height, we calculate it by means of the Pythagorean theorem that says the following

`\begin{gathered} c^2=a^2+b^2 \\ c=13 \\ a=5 \\ b=h \\ \text{replacing:} \\ 13^2=5^2+h^2 \\ h^2=13^2-5^2 \\ h=\sqrt[]{169-25} \\ h=\sqrt[]{144}=12 \end{gathered}`

The height is 12 cm

The volume is:

`\begin{gathered} V=(1)/(3)\cdot3.14\cdot5^2\cdot12 \\ V=314 \end{gathered}`

The water bottle has a total of 500 cubic centimeters, while the cone is 314 cubic centimeters, therefore it cannot pour out all the water and it would overflow