Volume is the amount of space occupied by a three-dimensional object. Some examples of three-dimensional figures include cubes, rectangular prisms, triangular prisms, cones, cylinders, and spheres. When finding the volume of a shape, the right units are important. There's a big difference between 9 ft, 9 ft², and 9 ft³. Because we're dealing with volume, our units will always be in cubic units, like in³, ft³, m³, etc.
The formula to solve for a rectangular prism’s volume is length x width x height. Making sure to use the right units, what is the volume of a rectangular prism with the following dimensions?
A
168 ft
B
168f³
C
188ft²
D
188ft³
To find the volume of a rectangular prism, we use the formula length x width x height.
Given:
Length = 8 ft
Width = 7 ft
Height = 3 ft
Volume = 8 ft x 7 ft x 3 ft
Volume = 168 ft³
So, the correct answer is B) 168 ft³.
A cylinder has two flat circular faces and one curved face. To solve for a cylinder’s volume, we first solve for the area of one of its circular faces using the formula πr², where r is the radius. Once we have the area of the circular face, we can multiply it by the cylinder’s height to get its volume.
If a cone and a cylinder have the same height and a circular face with the same dimensions, then the volume of the cone will always be ⅓ of the volume of the cylinder. So the formula for a cone’s volume is ⅓ x πr² x h.
If the volume of a cylinder is 75.4 in³, which of the following equations can we use to solve for the volume of a cone with the same dimensions as the cylinder?
A
75.4 x ½
B
75.4 x 2
C
75.4 x ⅓
D
75.4 x 3
If the volume of a cylinder is 75.4 in³, we know that the volume of a cone with the same dimensions as the cylinder will be ⅓ of the cylinder's volume.
So, to find the volume of the cone, we can use the equation:
Volume of cone = 75.4 in³ x ⅓
Volume of cone = 25.133 in³
Therefore, the correct equation to solve for the volume of the cone with the same dimensions as the cylinder is C) 75.4 x ⅓.