Find the total surface area of hemisphere of radius 10cm ?
Solution : Here radius = 10 cm We know that the surface area of hemisphere = \(3 \pi r^2\) = \(3 \times 3.14 \times 10 \times 10\) = 942 \(cm^2\)
Surface Area of Hemisphere – Formula and Examples
Here you will learn what is the formula for surface area of hemisphere (total and curved surface area of hemisphere) with examples. Let’s begin – What is Hemisphere ? Let us take a solid sphere, and slice it exactly ‘through the middle’ with a plane that passes through its centre. It gets divided into two …
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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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Formula for Volume of Cone with Examples
Here you will learn what is the formula for volume of cone and examples based on it. Let’s begin – What is Cone ? A cone is a solid which has a circle at its base and a slanting lateral surface that converges at the apex. Its dimensions are defined by the radius of the …
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. …
Surface Area of Cone – Formula and Examples
Here you will learn formula for the curved surface area and total surface area of cone and its derivation with examples. Let’s begin – What is Cone ? A cone is a solid which has a circle at its base and a slanting lateral surface that converges at the apex. Its dimensions are defined by …
What is the Equation of Director Circle of Hyperbola ?
Solution : The locus of the intersection of tangents which are at right angles is known as director circle of the hyperbola. The equation to the director circle is : \(x^2+y^2\) = \(a^2-b^2\) If \(b^2\) < \(a^2\), this circle is real ; If \(b^2\) = \(a^2\) the radius of the circle is zero & it …
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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 …
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 …
