Question

if the ratio of radii of two spheres is 3 ratio 4 then what is the ratio of their volumes
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Answer 1

Answer:

ratios of area of Sphere equal to 3 is to 4.

volume of Sphere equal to

$4 \div 3 \times \pi \times {r}^{3}$

ratio of volumes of Sphere

$\frac{4 \div 3 \times \pi \times {3}^{3} }{4 \div 3 \times \pi \times {4}^{3} }$

$\frac{27}{64}$

27:64

Answer 2

$\huge\mathtt{\underline{ANSWER:-}}$

$\sf\implies 27:64$

$\huge\mathbb{\underline{\purple{SOLUTION:-}}}$

$\bold{Given}\begin{cases}\sf{Radii\:of\: spheres}\\ \sf{In\: ratio 4:3}\end{cases}$

$\mathbb{TO\: FIND:-}$

Ratio of their volumes

• Now let the radii be r

The radii be 3r and 4r

$\sf\implies r_1=3r\\ \\ \sf\implies r_2=4r$

• Now 1st find the volume of 1st sphere

$\mathfrak{\underline{ Volume\:of\:sphere=\frac{4}{3}\pi r{}^{3}}}$

$\sf Volume\:of\:sphere_1=\frac{4}{3}\pi r{}^{3}\\ \\ \sf\leadsto Volume\:of\:sphere_1=\frac{4}{3}\pi\times 27r{}^{3}\\ \\ \sf\implies or\: 27\frac{4}{3}\pi r{}^{3}$

$\sf\underline{\purple{Volume\:of\:sphere_1=27\frac{4}{3}\pi r{}^{3}}}$

$\sf Volume \:of\:sphere_2=\frac{4}{3}\pi r{}^{3}$

$\bold{Radius}\begin{cases}\sf{4r}\end{cases}$

$\sf Volume\:of\:sphere_2=\frac{4}{3}\pi\times 4r\times 4r\times 4r\\ \\ \sf\leadsto Volume\:of\:sphere_2=\frac{4}{3}\pi 64r{}^{3}\\ \\ \sf\implies or 64\frac{4}{3}\pi r{}^{3}$

$\sf\underline{\purple{Volume\:of\:sphere_2=64\frac{4}{3}\pi r{}^{3}}}$

$\sf\implies Ratio=\frac{Volume\:of\:sphere_1}{Volume\:of\:sphere_2}\\ \\ \sf\implies Ratio=\frac{27\cancel{\frac{4}{3}\pi r{}^{3}}}{64\cancel{\frac{4}{3}\pi r{}^{3}}}\\ \\ \sf\implies \frac{27}{64}\\ \\ \sf\Longrightarrow 27:64$

$\boxed{\sf{Ratio\:of\: their\: volumes=27:64}}$

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