A sphere of radius $r$ is inscribed inside a cube. The volume enclosed between the cube and the sphere is :

(16 - \frac{2 π}{3}) r^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(22 - \frac{2 π}{3}) r^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(8 - \frac{4 π}{3}) r^{3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(12 - \frac{4 π}{3}) r^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $(8 - \frac{4 π}{3}) r^{3}$
Side of cube $= 2 r$

The volume enclosed $=$ volume of cube $-$ volume of the sphere

$= (2 r)^{3} - \frac{4}{3} π r^{3}$

$= 8 r^{3} - \frac{4}{3} π r^{3}$

$= (8 - \frac{4 π}{3}) r^{3}$ .

Suggest Corrections

Similar questions

Find the average rate of change of density with respect to the radius of a sphere in the interval [2, 5], where the density in terms of radius, r, is given by $d (r) = 3 r^{3} + 9$

Q. If in a

△ A B C, r_{1} = 2 r_{2} = 3 r_{3},

then:

Q. In a

△ A B C

, if

r_{1} = 2 r_{2} = 3 r_{3}

, then

Q. A sphere of radius

3

, inscribed in a cube, is tangent to all six faces of the cube. The volume contained outside the sphere and inside the cube, in standard units, is:

Q. If the potential energy between electron and proton at a distance r is given by

U = - (\frac{k e^{2}}{3 r^{3}})

. The force is :

Join BYJU'S Learning Program

A sphere of radius r is inscribed inside a cube. The volume enclosed between the cube and the sphere is :

The correct option is C (8−4π3)r3Side of cube=2rThe volume enclosed = volume of cube − volume of the sphere=(2r)3−43πr3=8r3−43πr3=(8−4π3)r3.

A sphere of radius $r$ is inscribed inside a cube. The volume enclosed between the cube and the sphere is :

The correct option is C $(8 - \frac{4 π}{3}) r^{3}$
Side of cube $= 2 r$

The volume enclosed $=$ volume of cube $-$ volume of the sphere

$= (2 r)^{3} - \frac{4}{3} π r^{3}$

$= 8 r^{3} - \frac{4}{3} π r^{3}$

$= (8 - \frac{4 π}{3}) r^{3}$ .