Question

Jacob and his family make their first stop on their vacation.. The beach! Jacob and his little brother enter a sand castle competition. The rules of the competition are 1. You can use any object that you bring yourself 2. You must use between 4000 and 14500 cubic inches of sand Below are all of the items that jacob and his brother will use to build their castle. For each item, calculate the volume of sand that each will hold

Answer 1

Answer with Explanation:

We have to find the volume of the (i) can and (ii) a cone, the volumes of the two shapes are as follows:

(i) Can:

The fomula for the volume of a cylinder (can) as well as the calculations for the volume are as follows:

`\begin{gathered} V=\pi r^2h \\ r=(3)/(2)in \\ h=5in \\ \therefore\rightarrow \\ V=\pi((3)/(2)in)^2(5in) \\ V=(45\pi)/(4)in^3 \\ V=35.343in^3 \end{gathered}`

(ii) Cone:

The formula for the cone as well as the calculations for the volume are as follows:

`\begin{gathered} V=\pi r^2(h)/(3) \\ r=3in \\ h=5in \\ \therefore\rightarrow \\ V=\pi((3)/(2)in)^2*((5in))/(3) \\ V=(45)/(12)\pi in^3 \\ V=11.789in^3 \end{gathered}`