Question

Two prisms are similar.• The height of the first prism is 2 cm.• The height of the second prism is 5 cm.• The width of the first prism is 4 cm.• The surface area of the first prism is 52 square cm.• The volume of the first prism is 24 cubic cm.The width of the second prism is 10cm.The surface area of the second prism issquare cm.The volume of the second prism is 475cubic cm.Blank 1: 10IBlank 2:Blank 3: 475

Answer 1

Step 1: Concept/Formula

`\text{Volume of a prism = Length x Width x Height}`

Step 1: Given data

First Prism

Height = 2cm

Width = 4cm

Length = ?

Volume = 24 cubic cm

Step 2:

Find the length of the first prism using the volume formula.

`\begin{gathered} \text{Volume of the first prism = Length x Width x Height} \\ 24\text{ = 2 x 4 x L} \\ 24\text{ = 8L} \\ L\text{ = }(24)/(8) \\ L\text{ = 3cm} \end{gathered}`

Step 3: Similarity property

`\begin{gathered} S\text{ince the two figures are similar, the ratio of their corresponding sides } \\ \text{are proportional.} \\ \frac{Length\text{ of 1}}{\text{Length of 2}}\text{ = }\frac{Width\text{ of 1}}{\text{Width of 2}}\text{ = }\frac{Heigth\text{ of 1}}{\text{Heigth of 2}} \end{gathered}`

Step 4: To find the width of the second prism, apply the ratio formula above

`\begin{gathered} \frac{Heigth\text{ of 1}}{\text{Height of 2}}\text{ = }\frac{Width\text{ of 1}}{\text{Width of 2}} \\ (2)/(5)\text{ = }(4)/(w) \\ \text{Cross multiply} \\ 2w\text{ = 20} \\ \text{Divide through by 2} \\ w\text{ = }(20)/(2) \\ w\text{ = 10 cm} \end{gathered}`

The width of the second prism = 10cm

Step 5: Find the length of prism 2

`\begin{gathered} \frac{Height\text{ of 1}}{\text{Height of 2}}\text{ = }\frac{Length\text{ of 1}}{\text{Length of 2}} \\ (2)/(5)\text{ = }(3)/(L) \\ \text{Cross multiply} \\ 2L\text{ = 15} \\ L\text{ = }(15)/(2)\text{ cm} \end{gathered}`

Step 6: Find the surface area of Prism 2

`\begin{gathered} \text{Surface area = 2LW + 2LH + 2WH} \\ =\text{ 2}*(15)/(2)*10\text{ + 2}*(15)/(4)*5\text{ + 2}*10*5 \\ =\text{ }(2*15*10)/(2)\text{ + }(2*15*5)/(2)\text{ + 100} \\ =\text{ 150 + 75 + 100} \\ =325cm^2 \end{gathered}`

Step 7; Volume of the second prims

`\begin{gathered} \text{Volume of the second prism = L x W x H} \\ =\text{ }(15)/(2)\text{ x 10 x 5} \\ =\text{ }(750)/(2) \\ =375cm^{3^{}} \end{gathered}`