Simplify: (7x4 – 7x3 + 7x2 + 2x) + (-5x4 + 7x3 + 5x2 – 9)
1 answer:
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Answer:
The funnel will fill the container in about 10 times
Step-by-step explanation:
To solve this question, the principal thing to do is to calculate the volumes of the cone-shaped funnel and the cylinder to actually know the number of times we will need to fill the funnel so as to fill the cylinder,
These number of times can simply be calculated by dividing the volume of the cylinder by the volume of the cone-shaped funnel.
Mathematically, we proceed as follows;
Volume of the cone funnel = 1/3 ×π× × h, where r and h represents the radius and height of the cone respectively.
From the question D = 6 inches, and mathematically r = D/2 = 6/2 = 3 inches and h = 7 inches
Plugging the values we have in the question, the volume = 1/3 ×π××7 = 21π
For the cylindrical receptacle, we have the volume calculated as π× × h
Where r = 4 inches and h = 13 inches.
Plugging these values we have ; π × × 13 = 208π
Now the number of times is simply = volume of cylindrical container/volume of cone-shaped funnel
= 208π/21π = 208/21 = 9.9 which is approximately 10 times