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(C) When a sphere of radius $r$ is divided into $4$ identical parts (by cutting it along two perpendicular planes passing through the center),each par

Vedclass · Accepted Answer

$8 \pi r^{2}$ square units

Vedclass · Answer

(C) When a sphere of radius $r$ is divided into $4$ identical parts (by cutting it along two perpendicular planes passing through the center),each part is a spherical wedge (specifically,a spherical quadrant).$1$. The curved surface area of the original sphere is $4 \pi r^{2}$. Since the sphere is divided into $4$ equal parts,the curved surface area of each part is $\frac{1}{4} 	imes 4 \pi r^{2} = \pi r^{2}$.$2$. The total curved surface area of all $4$ parts is $4 	imes \pi r^{2} = 4 \pi r^{2}$.$3$. Each of the $4$ parts has two flat semi-circular faces created by the cuts. Since there are $4$ parts,there are $4 	imes 2 = 8$ semi-circular faces in total.$4$. The area of one semi-circular face is $\frac{1}{2} \pi r^{2}$.$5$. The total area of these $8$ flat faces is $8 	imes \frac{1}{2} \pi r^{2} = 4 \pi r^{2}$.$6$. The total surface area of the $4$ parts is the sum of the total curved surface area and the total flat surface area:Total Surface Area $= 4 \pi r^{2} + 4 \pi r^{2} = 8 \pi r^{2}$ square units.

If a sphere of radius $r$ is divided into $4$ identical parts,then the total surface area of the $4$ parts is

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