The height is increasing at the rate of (6/5π) ft/min.
It is given that Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min. Also, its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal.
For this, we need to find the volume of a cone. Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.
The volume of a cone is - V=1/3hπr²
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Answer: first option
Step-by-step explanation:
The volume of a regular pyramid can be calculated with the following fromula:
Where B is the area of the base of the pyramid and h iis the height of the pyramid.
The base is a square, therefore, its area B is:
You know that the height is 3, therefore, you can substitute these values into the formula.
THerefore, the volume of the pyramid is:
a. First five terms: 9,13,17,21,25
b. Sum of first 25 terms = 1425
c. The given sequence is an arithmetic sequence because the common difference between two consecutive terms is same.
Further explanation:
Given
Formula of sequence
<u>1. First 5 terms:</u>
For first 5 terms, we have to put n=1,2,...5,
So,
<u>2. Sum of first 25 terms:</u>
For that we have to find 25th term first
The formula for sum is:
<u>3. Type of sequence</u>
The given sequence is an arithmetic sequence because the common difference between two consecutive terms is same.
i.e.
Keywords: Arithmetic sequence, Sum of arithmetic sequence
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