Question

Answer this volume based Question. I will make uh brainliest + 50 points​

Answer 1

Answer:

$\huge{\purple {r= 2\times\sqrt[3]3}}$

$\huge 2\times \sqrt [3]3 = 2.88$

Step-by-step explanation:

• For solid iron sphere:
• radius (r) = 2 cm (Given)

• Formula for $V_{sphere}$ is given as:

• $V_{sphere} =\frac{4}{3}\pi r^3$

• $\implies V_{sphere} =\frac{4}{3}\pi (2)^3$

• $\implies V_{sphere} =\frac{32}{3}\pi \:cm^3$

• For cone:
• r : h = 3 : 4 (Given)
• Let r = 3x & h = 4x

• Formula for $V_{cone}$ is given as:

• $V_{cone} =\frac{1}{3}\pi r^2h$

• $\implies V_{cone} =\frac{1}{3}\pi (3x)^2(4x)$

• $\implies V_{cone} =\frac{1}{3}\pi (36x^3)$

• $\implies V_{cone} =12\pi x^3\: cm^3$

• It is given that: iron sphere is melted and recasted in a solid right circular cone of same volume
• $\implies V_{cone} = V_{sphere}$

• $\implies 12\cancel{\pi} x^3= \frac{32}{3}\cancel{\pi}$

• $\implies 12x^3= \frac{32}{3}$

• $\implies x^3= \frac{32}{36}$

• $\implies x^3= \frac{8}{9}$

• $\implies x= \sqrt[3]{\frac{8}{3^2}}$

• $\implies x={\frac{2}{ \sqrt[3]{3^2}}}$

• $\because r = 3x$

• $\implies r=3\times {\frac{2}{ \sqrt[3]{3^2}}}$

• $\implies r=3\times 2(3)^{-\frac{2}{3}}$

• $\implies r= 2\times (3)^{1-\frac{2}{3}}$

• $\implies r= 2\times (3)^{\frac{1}{3}}$

• $\implies \huge{\purple {r= 2\times\sqrt[3]3}}$
• Assuming log on both sides, we find:

• $log r = log (2\times \sqrt [3]3)$

• $log r = log (2\times 3^{\frac{1}{3}})$

• $log r = log 2+ log 3^{\frac{1}{3}}$

• $log r = log 2+ \frac{1}{3}log 3$

• $log r = 0.4600704139$

• Taking antilog on both sides, we find:

• $antilog(log r )= antilog(0.4600704139)$

• $\implies r = 2.8844991406$

• $\implies \huge \red{r = 2.88\: cm}$

• $\implies 2\times \sqrt [3]3 = 2.88$