285,598 views
27 votes
27 votes
A toy house has the dimension as shown below. A hobbyist has a bottle of paint that can cover a total of 1000 square centimeters. If the bottle of paint is full when the hobbyist starts painting, what percentage of the bottle is used to cover the entire house except for the bottom of the rectangular prism?

A toy house has the dimension as shown below. A hobbyist has a bottle of paint that-example-1
User Alix Axel
by
3.2k points

1 Answer

26 votes
26 votes

Calculate the area of each face that is covered by the paint:

Area of 1 and 4:

Use Pythagorean theorem to find 1/2 b:


\begin{gathered} (1)/(2)b=\sqrt[]{(5\operatorname{cm})^2-(4\operatorname{cm})^2} \\ \\ (1)/(2)b=\sqrt[]{25\operatorname{cm}^2+16cm^2} \\ \\ (1)/(2)b=\sqrt[]{41cm^2} \\ \\ b=2\sqrt[]{41}cm \\ \\ \\ A_1=A_4=(1)/(2)b\cdot h \\ \\ A_1=A_4=(1)/(2)(2\sqrt[]{41}cm)(4\operatorname{cm}) \\ \\ A_1=A_4=4\sqrt[]{41}cm^2 \end{gathered}

Area of 2 and 3:


\begin{gathered} A_2=A_3=w\cdot l \\ \\ A_2=A_3=5\operatorname{cm}\cdot9\operatorname{cm} \\ \\ A_2=A_3=45cm^2 \end{gathered}

Area of 5 and 7:


\begin{gathered} A_5=A_7=w\cdot l \\ \\ \\ A_5=A_7=6\operatorname{cm}\cdot7\operatorname{cm} \\ \\ A_5=A_7=42\operatorname{cm} \end{gathered}

Area of 6 and 8:


\begin{gathered} A_6=A_8=w\cdot l \\ \\ A_6=A_8=9\operatorname{cm}\cdot7\operatorname{cm} \\ \\ A_6=A_8=63\operatorname{cm}^2 \end{gathered}

Then, the total area cover by the paint is:


\begin{gathered} A_T=A_1+A_2+A_3+A_4+A_5+A_6+A_7+A_8_{} \\ \\ A_T=(4\sqrt[]{41}+45+45+4\sqrt[]{41}+42+63+42+63)cm^2 \\ \\ A_T=(300+8\sqrt[]{41})cm^2 \\ \\ A_T\approx351.2\operatorname{cm}^2 \end{gathered}If the paint can cover 1000 square centimeters the percentage used to cover the entire house is: 35.12%
351.2\operatorname{cm}\cdot\frac{100}{1000\operatorname{cm}^2}=35.12

A toy house has the dimension as shown below. A hobbyist has a bottle of paint that-example-1
A toy house has the dimension as shown below. A hobbyist has a bottle of paint that-example-2
A toy house has the dimension as shown below. A hobbyist has a bottle of paint that-example-3
User Fire Lancer
by
2.7k points