A right hexagonal prism is enlarged by a scale factor of 5.7
a) Determine the value of Volume of Large Prism over the Volume of the small Prism
Do Not Round
b) Determine the value of Surface area of Large Prism over the Surface area of Small Prism Do Not Round
volume grows by the scale factor ^3
area grows as the scale factor ^2
So, if the original smaller prism has volume V, then the larger prism has volume 5.7^3 * V
Similarly for the areas.
I don't understand, could you please explain further?
To determine the values of volume and surface area, we need the formula for a right hexagonal prism.
The volume of a right hexagonal prism is given by the formula:
Volume = 3√3 * s^2 * h, where s is the length of the side of the hexagon and h is the height of the prism.
The surface area of a right hexagonal prism is given by the formula:
Surface Area = 6 * s * h + 3 * √3 * s^2, where s is the length of the side of the hexagon and h is the height of the prism.
Given that the prism is enlarged by a scale factor of 5.7:
a) Volume ratio:
The scale factor for volume is the cube of the linear scale factor. So, the volume ratio will be (5.7)^3.
b) Surface area ratio:
The scale factor for surface area is the square of the linear scale factor. So, the surface area ratio will be (5.7)^2.
To determine the values of the Volume and Surface area of the large prism compared to the small prism, we need to understand the relationships between scale factor and volume/surface area.
Given that the prism is being enlarged by a scale factor of 5.7, it means that all sides of the prism - the height and base - are multiplied by 5.7.
a) To determine the value of Volume of the Large Prism over the Volume of the Small Prism, we need to remember that volume is calculated by multiplying the base area by the height.
The relationship between the scale factor and volume is that the volume is proportional to the cube of the scale factor. So, to find the ratio between the volumes, we can simply calculate the cube of the scale factor:
Volume Large Prism / Volume Small Prism = (scale factor)^3 = 5.7^3 = 185.193
Therefore, the value of Volume of the Large Prism over the Volume of the Small Prism is 185.193.
b) To determine the value of Surface area of the Large Prism over the Surface area of the Small Prism, we need to remember that surface area is calculated by adding the areas of all the individual faces.
The relationship between the scale factor and surface area is that the surface area is proportional to the square of the scale factor. So, to find the ratio between the surface areas, we can simply calculate the square of the scale factor:
Surface area Large Prism / Surface area Small Prism = (scale factor)^2 = 5.7^2 = 32.49
Therefore, the value of Surface area of the Large Prism over the Surface area of the Small Prism is 32.49.