The radii of three out of four spheres are 33 | vedclass

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(D) The surface area of a sphere is given by the formula $S = 4 \pi r^2$.Let the radii of the three spheres be $r_1 = 33 \, cm$,$r_2 = 44 \, cm$,and $

Vedclass · Accepted Answer

$73$

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(D) The surface area of a sphere is given by the formula $S = 4 \pi r^2$.Let the radii of the three spheres be $r_1 = 33 \, cm$,$r_2 = 44 \, cm$,and $r_3 = 48 \, cm$.Let the radius of the fourth sphere be $R$.According to the problem,the surface area of the fourth sphere is equal to the sum of the surface areas of the first three spheres:$4 \pi R^2 = 4 \pi r_1^2 + 4 \pi r_2^2 + 4 \pi r_3^2$Dividing both sides by $4 \pi$,we get:$R^2 = r_1^2 + r_2^2 + r_3^2$$R^2 = (33)^2 + (44)^2 + (48)^2$$R^2 = 1089 + 1936 + 2304$$R^2 = 5329$Taking the square root of both sides:$R = \sqrt{5329} = 73 \, cm$.Thus,the radius of the fourth sphere is $73 \, cm$.

The radii of three out of four spheres are $33 \, cm$,$44 \, cm$,and $48 \, cm$ respectively. If the surface area of the fourth sphere is equal to the sum of the surface areas of the first three spheres,find the radius of the fourth sphere (in $cm$).

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