Question

given the surface area of two similar prisms are 144cm^2 and 625cm^. if the height of the smaller prisms is 20cm, what is the height of the larger prism?a) 41.7b)86.8c)4.6d) 9.6 similarity ratio ( smaller:larger) _____:____

Answer 1

The height of the larger prism is;

`41.7\text{ cm}`

Step-by-step explanation:

Given that the surface area of two similar prisms are 144cm^2 and 625cm^2;

`\begin{gathered} A_1=144cm^2 \\ A_2=625cm^2 \end{gathered}`

Given that the height of the smaller prism is 20cm;

Since they are similar, the ratio between their area and heights can be expressed as;

`(h_2)/(h_1)=\sqrt[]{(A_2)/(A_1)}`
`h_2=h_1\sqrt[]{(A_2)/(A_1)}`

substituting the given values;

`\begin{gathered} h_2=h_1\sqrt[]{(A_2)/(A_1)} \\ h_2=20_{}\sqrt[]{\frac{625}{144_{}}} \\ h_2=41.66667 \\ h_2=41.7 \end{gathered}`

Therefore, the height of the larger prism is;

`41.7\text{ cm}`