mathemerize

Volume of Sphere and Hemisphere – Formula and Examples

Here you will learn what is the formula for volume of sphere and hemisphere with examples based on it. Let’s begin –  Formula for Volume of Sphere and Hemisphere (i) Volume of Sphere Formula Volume of sphere = \({4\over 3}\pi r^3\) where r is the radius of sphere. (ii) Volume of Hemisphere Formula Volume of …

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Formula for Surface Area of Sphere with Examples

Here you will learn what is the formula for surface area of sphere and examples based on it. Let’s begin – What is Sphere ? A sphere is a three dimensional figure (solid figure), which is made up of all points in the space, which lie at a constant distance called the radius, from a …

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What should be the height of the conical tent ?

Question : In a marriage ceremony of her daughter Poonam, Ashok has to make arrangements for the accommodation of 150 persons. For this purpose, he plans to build a conical tent in such a way that each person has 4 sq. meters of the space on ground and 20 cubic meters of air to breath. …

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What is the parametric equation of ellipse ?

Solution : The equation x = acos\(\theta\) & y = bsin\(\theta\) together represent the parametric equation of ellipse \({x_1}^2\over a^2\) + \({y_1}^2\over b^2\) = 1, where \(\theta\) is a parameter. Note that if P(\(\theta\)) = (acos\(\theta\), bsin\(\theta\)) is on the ellipse then ; Q(\(\theta\)) = (acos\(\theta\), bsin\(\theta\)) is on auxilliary circle. A circle described on …

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Differentiate \(x^{sinx}\) with respect to x.

Solution : Let y = \(x^{sinx}\). Then, Taking log both sides, log y = sin x.log x \(\implies\) y = \(e^{sin x.log x}\) By using logarithmic differentiation, On differentiating both sides with respect to x, we get \(dy\over dx\) = \(e^{sin x.log x}\)\(d\over dx\)(sin x.log x) \(\implies\) \(dy\over dx\) = \(x^{sin x}{log x {d\over dx}(sin …

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