Question

Compare the volume and surface area of a sphere with a radius of 2 cm with that of a cube that has sides measuring 3.22 cm.

Answers:
The volume of the sphere is approximately equal to the volume of the cube, but the sphere has a greater surface area.

The sphere and the cube have approximately the same volume and surface area.

The volume of the cube is greater than the volume of the sphere, but the sphere has a greater surface area.

The volume of the sphere is approximately equal to the volume of the cube, but the cube has a greater surface area.

Answer 1

For cube:-

• side=3.22cm

Volume=

$\\ \sf\longmapsto (3.22)^3=33.38cm^3$

Surface area:-

$\\ \sf\longmapsto 6(3.22)^2=62.2cm^2$

For Sphere-

• Radius=2cm

Volume:-

$\\ \sf\longmapsto \dfrac{4}{3}\pi (2)^3$

$\\ \sf\longmapsto \dfrac{4}{3}\pi 8$

$\\ \sf\longmapsto \dfrac{32\pi}{3}$

$\\ \sf\longmapsto 10.6\pi cm^3=33.284cm^3$

SUrface area:-

$\\ \sf\longmapsto 4\pi r^2$

$\\ \sf\longmapsto 4\pi (2)^2=16\pi$

$\\ \sf\longmapsto 50.24cm^2$

Option D is correct