The radii of two spheres are in the ratio 3:5 The ratio of their volumes is
$9 : 25$
$27 : 125$
$\sqrt{3} : \sqrt{5}$
$\sqrt[3]{3} : \sqrt[3]{5}$

Question

The radii of two spheres are in the ratio 3-5 The ratio of their volumes is9-2527-125displaystyle sqrt-3-sqrt-5-displaystyle sqrt-3-3-sqrt-3-5-

Toppr Admin · Accepted Answer

Ratio of radii - 3-5-x2234- Ratio of volumes-43-x3C0-r31-43-x3C0-r32-xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -33-53-xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -27-125

The radii of two spheres are in the ratio 3:5 The ratio of their volumes is9:2527:125√3:√53√3:3√5

Ratio of radii = 3:5∴ Ratio of volumes=43πr31:43πr32 =33:53 =27:125

The radii of two spheres are in the ratio 3:5 The ratio of their volumes is
$9 : 25$
$27 : 125$
$\sqrt{3} : \sqrt{5}$
$\sqrt[3]{3} : \sqrt[3]{5}$

Ratio of radii = $3 : 5$
$∴$ Ratio of volumes $=$ $\frac{4}{3} π r_{1}^{3} : \frac{4}{3} π r_{2}^{3}$
$= 3^{3} : 5^{3}$
$= 27 : 125$