What is the diameter of a sphere with a volume of 1352cm^(3), to the nearest tenth of a centimeter? Answer: cm

Identify formula for volume: Identify the formula to calculate the volume of a sphere. The formula for the volume (V) of a sphere in terms of its radius (r) is V = (4/3)πr³.Rearrange formula for radius: Rearrange the formula to solve for the radius. To find the radius, we need to rearrange the formula to solve for r. This gives us r = ((3V)/(4π))^(1/3).Substitute given volume: Substitute the given volume into the rearranged formula. We know the volume V = 1352 cm³, so we substitute this value into the formula to find the radius: r = ((3*1352 cm³)/(4π))^(1/3).Calculate radius: Calculate the radius using the substituted values. r = ((3*1352 cm³)/(4π))^(1/3) = ((4056 cm³)/(4π))^(1/3).Evaluate expression for radius: Evaluate the expression to find the radius. r ≈ ((4056 cm³)/(12.5664))^(1/3) ≈ (322.637 cm³)^(1/3) ≈ 6.879 cm (rounded to three decimal places for intermediate calculation).Calculate sphere diameter: Calculate the diameter of the sphere. The diameter (d) is twice the radius, so d = 2r. Therefore, d = 2 * 6.879 cm ≈ 13.758 cm.Round diameter to nearest tenth: Round the diameter to the nearest tenth of a centimeter. The diameter rounded to the nearest tenth is approximately 13.8 cm.

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What is the diameter of a sphere with a volume of
1352cm^(3), to the nearest tenth of a centimeter?
Answer:
cm

What is the diameter of a sphere with a volume of $1352 \mathrm{~cm}^{3}$ , to the nearest tenth of a centimeter? $\newline$ Answer: $\mathrm{cm}$

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Grade 7

Convert between customary and metric systems

Full solution

Q. What is the diameter of a sphere with a volume of

1352 \mathrm{~cm}^{3}

, to the nearest tenth of a centimeter?

\newline

Answer:

\mathrm{cm}

Identify formula for volume: Identify the formula to calculate the volume of a sphere. $\newline$ The formula for the volume $V$ of a sphere in terms of its radius $r$ is $V = \frac{4}{3}\pi r^3$ .
Rearrange formula for radius: Rearrange the formula to solve for the radius. $\newline$ To find the radius, we need to rearrange the formula to solve for $r$ . This gives us $r = \left(\frac{3V}{4\pi}\right)^{\frac{1}{3}}$ .
Substitute given volume: Substitute the given volume into the rearranged formula. $\newline$ We know the volume $V = 1352 \text{ cm}^3$ , so we substitute this value into the formula to find the radius: $r = \left(\frac{3 \times 1352 \text{ cm}^3}{4\pi}\right)^{\frac{1}{3}}$ .
Calculate radius: Calculate the radius using the substituted values. $\newline$ $r = \left(\frac{3\times 1352 \text{ cm}^3}{4\pi}\right)^{\frac{1}{3}} = \left(\frac{4056 \text{ cm}^3}{4\pi}\right)^{\frac{1}{3}}$ .
Evaluate expression for radius: Evaluate the expression to find the radius. $\newline$ $r \approx (\frac{4056 \text{ cm}^3}{12.5664})^{\frac{1}{3}} \approx (322.637 \text{ cm}^3)^{\frac{1}{3}} \approx 6.879 \text{ cm}$ (rounded to three decimal places for intermediate calculation).
Calculate sphere diameter: Calculate the diameter of the sphere. $\newline$ The diameter $d$ is twice the radius, so $d = 2r$ . Therefore, $d = 2 \times 6.879 \, \text{cm} \approx 13.758 \, \text{cm}$ .
Round diameter to nearest tenth: Round the diameter to the nearest tenth of a centimeter. $\newline$ The diameter rounded to the nearest tenth is approximately $13.8\,\text{cm}.$