Answer:
ΔV = 0.36π in³
Step-by-step explanation:
Given that:
The radius of a sphere = 3.0
If the measurement is correct within 0.01 inches
i.e the change in the radius Δr = 0.01
The objective is to use differentials to estimate the error in the volume of sphere.
We all know that the volume of a sphere
The differential of V with respect to r is:
dV = 4 πr² dr
which can be re-written as:
ΔV = 4 πr² Δr
ΔV = 4 × π × (3)² × 0.01
ΔV = 0.36π in³
Answer:
The volume of the rectangular prism is <u>19.25 inches³</u>.
Step-by-step explanation:
Given:
It takes 154 cubes with side lengths of 1/2 inch to fill a rectangular prism.
Now, to find the rectangular prism's volume.
We first find the volume of a cube to fill in the rectangular prism.
The side length of the cube =
Now, to get the volume of cube we put formula:
<em>Thus, the volume of a cube is </em><em />
<em>Number of cubes = 154.</em>
<u><em>According to question, it takes 154 cubes to fill the rectangular prism.</em></u>
<u><em>So, to get the volume of prism we need to find the volume of 154 cubes.</em></u>
Now, to get the volume of 154 such cubes we multiply the volume of a cube by number of cubes:
Therefore, the volume of the rectangular prism is 19.25 inches³.