Question

shape 1, the rectangular pyramid, is three times the volume of ice in shape 2, the triangularpyramid. Is All correct? Use the drop-down menus to explain your answer.Ice Molds5 cmA5 cm3 cm4cm3 cm4 cmShape 1Shape 2Click the arrows to choose an answer from each menu,cubic centimeters.The volume of ice in shape 1 is Choose..The volume of ice in shape 2 is Choose...Shape 1 contains choose...cubic centimeters.ice as shape 2All Choosecorrect

Answer 1

SOLUTION

To answer the questions, we nee to find the volume of both shapes

Shape 1 is a rectangular pyramid.

Volume of shape 1 is

$\begin{gathered} \text{Volume of a pyramid = }\frac{1}{3}\times base\text{ area }\times height\text{ } \\ The\text{ base of the rectangular pyramid is a rectangle } \\ \text{The base area = L }\times b=\text{ 3}\times4=12 \\ \text{The height h= 5} \\ \text{Volume of shape 1 = }\frac{1}{3}\times base\text{ area }\times height\text{ } \\ =\text{ }\frac{1}{3}\times12\text{ }\times5 \\ =\text{ 4 }\times5=20cm^3 \end{gathered}$

Volume of shape 2 is

$\begin{gathered} \text{The base of shape 2 is a triangle } \\ \text{Area of the base = }\frac{1}{2}bh \\ =\text{ }\frac{1}{2}\times4\times3\text{ = 6cm} \\ \text{Volume = }\frac{1}{3}\times base\text{ area }\times height\text{ } \\ \text{Volume = }\frac{1}{3}\times6\text{ }\times5 \\ \text{Volume = 2 }\times\text{ 5 } \\ \text{Volume of shape 2 = 10cm}^3 \end{gathered}$

Therefore,

The volume of ice in shape 1 is 20

The volume of ice in shape 2 is 10

Shape 1 contains twice or two times the ice in shape 2