Question

The red portion in the image is removed from the sphere to form a cavity. The centre of the base of the
cylindrical cavity and the sphere are the same. If the radius of the sphere is 6 cm and the height and
radius of the cavity are equal, what is the volume (in cms) of the cavity?​

Answer 1

Answer:

⇒ Draw a line segment AB=4.5cm

⇒ Take B as center and draw an angle of 60

⇒ Cut off BC=5.5cm

⇒ Take A as with radius 4.8cm and draw an arc.

⇒ Take C as with radius 5cm and draw an arc, which cuts off previous arc at point D

⇒ Join CD and AD.

Step-by-step explanation:

Answer 2

Answer:

volume of the cavity is $\pi 54\sqrt{2} }cm^{3}$

Step-by-step explanation:

Given a cavity is made that is of cylindrical shape in the sphere whose height(h) and radius(a) are equal.

And the center of base and sphere are same. Hence, applying the Pythagorean theorem, $a^{2} =r^{2} -h^{2}$

Radius of sphere, $r=6cm$

since a and h are equal, $r^{2} =2a^{2}$

                                 $\implies 6^{2} =2a^{2}\implies a =\sqrt{18}$

Volume of the cylinder cavity, $V=\pi a^{2} h$

                                                      $=\pi a^{3} =\pi (\sqrt{18} } )^{3}$

                                                      $=\pi 54\sqrt{2} }$

Therefore, the volume of the cavity is $\pi 54\sqrt{2} }cm^{3}$