The radii of five metal spheres are 1, cm, 3, | vedclass

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(A) $1$. Volume of a sphere is given by $V = \frac{4}{3}\pi r^3$. $2$. Total volume of the five spheres = $\frac{4}{3}\pi (1^3 + 3^3 + 4^3 + 5^3 + 8^3

Vedclass · Accepted Answer

$9\, cm, 27$

Vedclass · Answer

(A) $1$. Volume of a sphere is given by $V = \frac{4}{3}\pi r^3$. $2$. Total volume of the five spheres = $\frac{4}{3}\pi (1^3 + 3^3 + 4^3 + 5^3 + 8^3) = \frac{4}{3}\pi (1 + 27 + 64 + 125 + 512) = \frac{4}{3}\pi (729)$. $3$. Let the radius of the new large sphere be $R$. Then $\frac{4}{3}\pi R^3 = \frac{4}{3}\pi (729)$,which implies $R^3 = 729$,so $R = 9\, cm$. $4$. Volume of one cylinder = $\pi r^2 h = \pi (3^2)(4) = 36\pi\, cm^3$. $5$. Number of cylinders = $\frac{	ext{Total Volume}}{	ext{Volume of one cylinder}} = \frac{\frac{4}{3}\pi (729)}{36\pi} = \frac{972\pi}{36\pi} = 27$ cylinders.

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