Answer:
The effect it will have on the volume is;
The volume will be 8 times larger
Explanation:
The dimensions of the given prism are;
The length of the prism, l = 5 in.
The breadth of the prism, b = 5 in.
The slant height of the prism, = 4 in. by 5 in.
The height of the prism, h = 7 in.
The shape of the prism = Parallelepiped
The volume of a parallelepiped = Area of Base × Height of the prism
The base area of the parallelepiped = The length × Breadth of the parallelepiped
∴ The base area of the given parallelepiped = 5 in. × 5 in. = 25 in.²
The volume of the given parallelepiped, V₁ is found as follows;
V₁ = 5 in. × 5 in. × 7 in. = 25 in.² × 7 in. = 175 in.³
When a scale factor of 2 in applied to the dimensions of the prism, we have;
The new volume, V₂ = 2 × 5 in. × 2 × 5 in. × 2 × 7 in.
∴ V₂ = 2 × 2 × 2 × 5 in. × 5 in. × 7 in. = 8 × 5 in. × 5 in. × 7 in. = 8 × V₁
Therefore;
V₂ = 8 × V₁
The volume of the image of the object, V₂ after applying a scale factor of 2 is 8 times larger than the volume of the object, V₁.