Answer:
The formula V= h(lw-πr²) can be used to determine the volume of the shape
Step-by-step explanation:
This problem bothers on the mensuration of subtraction composite solid shapes.
To solve for the volume of a prism that had a cylinder cut from the middle
1. We need to solve for the volume of the rectangular prism
Let Vr be volume of rectangular prism
Vr= length x width x height
Vr= l*w*h
2. We need to solve for the volume of the cylinder
Let Vc be the volume of the cylinder
Vc= πr²h
3. Finally we have to subtract the volume of cylinder from volume of prism
V= Vr-Vc
V= l*w*h-πr²h
V= h(lw-πr²)
Where
h= the height of the prism and the cylinder
w= width of the prism
r= radius of the cylinder
l= length of the prism
Answer: The correct option is D; Find the volume of each 3D solid and determine the difference of the of the two volumes.
Step-by-step explanation: When you have a rectangular prism, what you have in effect is a cuboid. The fact that a cylinder was cut out of it makes it a solid figure.
The volume of a rectangular prism (or cuboid) is given as;
Volume of Rectangular prism = L x W x H
Where L is the length, W is the width and H is the height.
Also a cylinder has its volume given as;
Volume of cylinder = π x r² x h
Where r is radius of the base circle, π (that is Pi) is usually given as 3.14, and h is the vertical height of the cylinder.
Since the cylinder has been cut out of the solid rectangular prism, the volume of the prism can now be derived as the difference between both solid shapes, that is, difference of both volumes as derived above.
