Question

how do you find the surface area and volume of a large prism X compaired to a similar smaller prism Y the scale factor is 1:3 prism Y has a surface area of 125.5 m squared and a volume of 87 m cubed

Answer 1

how do you find the surface area and volume of a large prism X compared to a similar smaller prism Y the scale factor is 1:3 prism Y has a surface area of 125.5 m squared and a volume of 87 m cubed.

The square-cube law can be stated as follows:

When an object undergoes a proportional increase in size, its new volume is proportional to the cube of the multiplier and its new surface area is proportional to the square of the multiplier.

Represented mathematically:

$$V _ {2} = V _ {1} \left(\frac {l _ {2}}{l _ {1}}\right) ^ {3}$$

where $V_{1}$ is the original volume, $V_{2}$ is the new volume, $l_{1}$ is the original length and $l_{2}$ is the new length.

$$A _ {2} = A _ {1} \left(\frac {l _ {2}}{l _ {1}}\right) ^ {2}$$

where $A_{1}$ is the original area, $A_{2}$ is the new area

In our case $\frac{l_2}{l_1} = 3$ - the scale factor

$$V _ {2} = 8 7 * 3 ^ {3} m ^ {3} = 2 3 4 9 m ^ {3}$$ $$A _ {2} = 1 2 5. 5 * 3 ^ {2} = 1 1 2 9. 5 m ^ {2}$$

Answer: surface area and volume equal $1129.5 \, m^2$ and $2349 \, m^3$