Alex has a block of wood that is in the shape of a prism with the dimensions shown. He cuts a 10-cm square hole through the center of the prism. What is the volume of the remaining solid?
Note: image is not drawn to scale.
The volume of the remaining solid is
cm3.
Note: image is not drawn to scale.
The volume of the remaining solid is
cm3.
Answers & Comments
Answer:
The volume of the original prism is:
V = lwh = (20 cm)(15 cm)(10 cm) = 3000 cm³
To find the volume of the remaining solid, we need to subtract the volume of the hole from the original volume. The hole has a height of 10 cm and a square base with side length 10 cm, so its volume is:
Vhole = (10 cm)²(10 cm) = 1000 cm³
Therefore, the volume of the remaining solid is:
Vremaining = V - Vhole = 3000 cm³ - 1000 cm³ = 2000 cm³
So the volume of the remaining solid is 2000 cubic centimeters.