Question

if the diameter of a sphere is equal to the side of a cube, find the ratio of their volumes​

Answer 1

Answer:

11/21

Step-by-step explanation:

$4 \div 3 \times d \div 2 \times d \div 2 \times d \div 2 \times \pi$

is volume of sphere

$d \times d \times d$

is volume of cube with side equal to diameter of sphere

therefore after cutting every common factor we get answer as 11/21

Answer 2

$d$ - the diameter of a sphere

$a$ - the side of a cube

$d=a\\\\V_{\text{sphere}}=\dfrac{4}{3}\pi r^3\\V_{\text{cube}}=a^3\\\\d=2r \implies a=2r\\\\V_{\text{cube}}=(2r)^3=8r^3\\\\\dfrac{V_{\text{cube}}}{V_{\text{sphere}}}=\dfrac{8r^3}{\dfrac{4}{3}\pi r^3}\\\\\dfrac{V_{\text{cube}}}{V_{\text{sphere}}}=\dfrac{6}{\pi}$

or the other way round

$\dfrac{V_{\text{sphere}}}{V_{\text{cube}}}=\dfrac{\pi}{6}$