Mathematics

If the volume of two spheres is in the ratio 27: 64, then the ratio of their radii is:
3 : 4
4 : 3
9 : 16
16 : 9

Mensuration

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Answer

Given, the volume of two spheres = 27: 64

By formula, volume of a sphere = $\dfrac{4πr^3}{3}$ , where r is the radius of the sphere.

Let r and R be the radii of the two spheres.

$\Rightarrow \dfrac{\dfrac{4πr^3}{3}}{\dfrac{4πR^3}{3}} = \dfrac{27}{64} \\[1em] \Rightarrow \dfrac{r^3}{R^3} = \dfrac{27}{64} \\[1em] \Rightarrow \dfrac{r}{R} = \dfrac{\sqrt[3]{27}}{\sqrt[3]{64}} \\[1em] \Rightarrow \dfrac{r}{R} = \dfrac{3}{4}.$

Hence, option 1 is the correct option.

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Mathematics

If the volume of two spheres is in the ratio 27: 64, then the ratio of their radii is:3 : 44 : 39 : 1616 : 9

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If the volume of two spheres is in the ratio 27: 64, then the ratio of their radii is:
3 : 4
4 : 3
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16 : 9

Assertion (A): If sin² A + sin A = 1 then cos⁴ A + cos² A = 1.
Statement 2: 1 - sin² A = cos² A
(A) is true, (R) is false.
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Both (A) and (R) are true, and (R) is the incorrect reason for (A).

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15 cm
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30 cm

The marked price of an article is ₹1,375. If the CGST is charged at a rate of 4%, then the price of the article including GST is:
₹55
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