QuestionJuly 17, 2025

40. If a spherical bubble has a volume of 972pi cm^3 , calculate the surface area of the bubble. Surface Area= sqrt (x)cm^2

40. If a spherical bubble has a volume of 972pi cm^3 , calculate the surface area of the bubble. Surface Area= sqrt (x)cm^2
40. If a spherical bubble has a volume of 972pi cm^3 , calculate the
surface area of the bubble.
Surface Area= sqrt (x)cm^2

Solution
4.1(300 votes)

Answer

18\sqrt{\pi} \, \text{cm}^2 Explanation 1. Calculate the radius Use the formula for the volume of a sphere: V = \frac{4}{3}\pi r^3. Set 972\pi = \frac{4}{3}\pi r^3 and solve for r: r^3 = \frac{972 \times 3}{4} = 729, so r = \sqrt[3]{729} = 9 cm. 2. Calculate the surface area Use the formula for the surface area of a sphere: A = 4\pi r^2. Substitute r = 9: A = 4\pi (9)^2 = 324\pi cm². 3. Find the square root of the surface area \sqrt{324\pi} cm² is the required form. Simplify: \sqrt{324\pi} = \sqrt{324} \times \sqrt{\pi} = 18\sqrt{\pi} cm².

Explanation

1. Calculate the radius<br /> Use the formula for the volume of a sphere: $V = \frac{4}{3}\pi r^3$. Set $972\pi = \frac{4}{3}\pi r^3$ and solve for $r$: $r^3 = \frac{972 \times 3}{4} = 729$, so $r = \sqrt[3]{729} = 9$ cm.<br />2. Calculate the surface area<br /> Use the formula for the surface area of a sphere: $A = 4\pi r^2$. Substitute $r = 9$: $A = 4\pi (9)^2 = 324\pi$ cm².<br />3. Find the square root of the surface area<br /> $\sqrt{324\pi}$ cm² is the required form. Simplify: $\sqrt{324\pi} = \sqrt{324} \times \sqrt{\pi} = 18\sqrt{\pi}$ cm².
Click to rate:

Similar Questions