The side of a cube is equal to diameter of the sphere. The ratio of volumes
of cube and sphere is

\frac{11}{12}

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\frac{22}{11}

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\frac{11}{21}

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\frac{21}{11}

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Solution

The correct option is D $\frac{21}{11}$
Let the sides of cube be $s$ and radius of sphere be $r$
then $s = 2 r = (2 r)^{3} = 8 r^{3}$
Volume of a cube $= s^{3}$
Volume of a sphere $= \frac{4}{3} π r^{3}$
Ratio of volume of cube and sphere $= \frac{8 r^{3}}{\frac{4}{3} π r^{3}}$
$= \frac{8 r^{3}}{\frac{4}{3} \times \frac{22}{7} r^{3}} = \frac{21}{11}$

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Similar questions

Q. A sphere and a cube are of the same height. The ratio of their volumes is

(a) 3 : 4

(b) 21 : 11

(c) 4 : 3

(d) 11 : 21

Q. Find the cubes of:
(i) −11
(ii) −12
(iii) −21

If $Δ ∣ ∣ ∣ ∣ \begin{matrix} a_{11} & a_{12} & a_{13} a_{21} & a_{22} & a_{23} a_{31} & a_{32} & a_{33} \end{matrix} ∣ ∣ ∣ ∣$ and $A_{i j}$ is cofactor of $a_{i j}$ , then value of $Δ$ is given by

a) $a_{11} A_{31} + a_{12} A_{32} + a_{13} A_{33}$
b) $a_{11} A_{11} + a_{12} A_{21} + a_{13} A_{31}$
c) $a_{21} A_{11} + a_{22} A_{12} + a_{23} A_{13}$
d) $a_{11} A_{11} + a_{21} A_{21} + a_{31} A_{31}$

Q. A sphere is melted and half of the molten liquid is used to form

11

identical cubes, whereas the remaining half is used to form

7

identical smaller spheres. The ratio of the side of the cube to the radius of the new small sphere is -

Question 80 (ii)

Find the product of $\frac{- 22}{11}$ and $\frac{- 21}{11}$ .

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The side of a cube is equal to diameter of the sphere. The ratio of volumes of cube and sphere is

The correct option is D 2111Let the sides of cube be s and radius of sphere be rthen s=2r=(2r)3=8r3Volume of a cube=s3Volume of a sphere=43πr3Ratio of volume of cube and sphere=8r343πr3=8r343×227r3=2111

The side of a cube is equal to diameter of the sphere. The ratio of volumes
of cube and sphere is