Of all open tanks in the form of a rectangular parallelopiped with a square.base having a fixed volume, the one that has the least inner surface area has the property that its
- depth in half of the base side
- depth is twice the base side
- depth is equal to the base side
- depth is one-third of the base side
The Correct Option is C
Solution and Explanation
Volume $(V) = l^2h \, \, \, \, \, \, \, \, \, \, \, $ ...(i)
and surface area, $(S) = 2(l^2+ hl + lh) S = 2l^2 + 4hl \, \, \, \, \, \, \, \, $.....(ii)
differentiating (i) w.r.t. h, we.get
$\frac{dV}{dh} =2lh \frac{dl}{dh}+l^{2}$
$ \Rightarrow 2lh \frac{dl}{dh} + l^{2} =0 $
$\Rightarrow \frac{dl}{dh} =- \frac{l}{2h} $
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Concepts Used:
Statistics
Statistics is a field of mathematics concerned with the study of data collection, data analysis, data interpretation, data presentation, and data organization. Statistics is mainly used to acquire a better understanding of data and to focus on specific applications. Also, Statistics is the process of gathering, assessing, and summarising data in a mathematical form.
Mathematically there are two approaches for analyzing data in statistics that are widely used:
Descriptive Statistics -
Using measures of central tendency and measures of dispersion, the descriptive technique of statistics is utilized to describe the data collected and summarise the data and its attributes.
Inferential Statistics -
This statistical strategy is utilized to produce conclusions from data. Inferential statistics rely on statistical tests on samples to make inferences, and it does so by discovering variations between the two groups. The p-value is calculated and differentiated to the probability of chance() = 0.05. If the p-value is less than or equivalent to, the p-value is considered statistically significant.