Question

If the ratio of the surface area of ​​two solid spheres is 25:16, then the volume of both is the same​

Answer 1

Answer:

no the volume will not be the same

Step-by-step explanation:

first take the value x if the ratios and dind out the radius of spheres nd then calculate the volume

Answer 2

Final Answer: The volume of both the sphere is 125:64

Step-by-step explanation:

The ratio of the surface area of two solid spheres is 25:16

Let the area of the first sphere and second sphere be A₁ and A₂ respectively.

A₁ : A₂ = 25:16

$\frac{A1}{A2} = \frac{25}{16}$

We know that area of the sphere, A = 4πr²

${\frac{4\pi r_{1} ^2}{4\pi r_{2}^2 } = \frac{25}{16}$

$\frac{r_{1}^2 }{r_{2}^2} = \frac{25}{16}$

$\frac{r_{1} }{r_{2} } = \frac{\sqrt{25}}{\sqrt{16} } \\\frac{r_{1} }{r_{2} } = \frac{5}{4}$

The volume of the sphere, V = $\frac{4\pi r^3}{3}$

Let the volume of the first sphere and second sphere be V₁ and V₂ respectively.

$\frac{V_{1} }{V_{2} } = \frac{\frac{4\pi r_{1} ^3}{3} }{\frac{4\pi r_{2} ^3}{3} } \\\frac{V_{1} }{V_{2} } =\frac{ r_{1} ^3}{r_{2}^3 } \\\frac{V_{1} }{V_{2} } = \frac{5^3}{4^3} \\\frac{V_{1} }{V_{2} } = \frac{125 }{64}$

So, the volume of both the spheres is 125:64.