1. The volume of a sphere can be found using the formula V = (4/3) * pi * r^3, where r is the radius of the sphere and pi is a constant approximately equal to 3.14159.
2. To find the volume of a sphere with a radius of 5 cm, we can substitute the radius into the formula: V = (4/3) * pi * (5 cm)^3 = (4/3) * 3.14159 * 125 cm^3 = 523.599 cm^3.
3. To find the radius of a sphere with a volume of 1000 cm^3, we can rearrange the formula to solve for the radius: r = ((3 * V) / (4 * pi)) ^ (1/3) = ((3 * 1000 cm^3) / (4 * 3.14159)) ^ (1/3) = (3000 / 12.56636) ^ (1/3) = (238.732 cm^3) ^ (1/3) = 6.32 cm (rounded to two decimal places).
4. If the volume of a sphere is multiplied by 8, the resulting volume is (8 * V) = (8 * (4/3) * pi * r^3) = (32/3) * pi * r^3. So the volume is multiplied by a factor of 32/3 or approximately 10.6667. This means that the new volume is approximately 10.6667 times the original volume.
VOLUME OF SPHERES QUICK CHECK ANSWERS
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2. To find the volume of a sphere with a radius of 5 cm, we can substitute the radius into the formula: V = (4/3) * pi * (5 cm)^3 = (4/3) * 3.14159 * (125 cm^3) = 523.59833 cm^3 (rounded to five decimal places).
3. To find the radius of a sphere with a volume of 1000 cm^3, let's solve for the radius in the formula V = (4/3) * pi * r^3. Rearranging the formula, we have r^3 = (3 * V) / (4 * pi). Taking the cube root of both sides, we get r = (3V / (4pi))^(1/3). Substituting V = 1000 cm^3 and pi ≈ 3.14159, we have r = (3 * 1000 cm^3 / (4 * 3.14159))^(1/3) ≈ (3000 / 12.56636)^(1/3) ≈ (238.732 cm^3)^(1/3) ≈ 6.33 cm (rounded to two decimal places).
4. If the volume of a sphere is multiplied by 8, the resulting volume is (8 * V) = (8 * (4/3) * pi * r^3) = (32/3) * pi * r^3. So the volume is multiplied by a factor of 32/3 or approximately 10.6667. This means that the new volume is approximately 10.6667 times the original volume.
2. To find the volume of a sphere with a radius of 5 cm, we can substitute the radius into the formula: V = (4/3) * pi * (5 cm)^3 = (4/3) * 3.14159 * (125 cm^3) = 523.59833 cm^3 (rounded to five decimal places).
3. To find the radius of a sphere with a volume of 1000 cm^3, let's solve for the radius in the formula V = (4/3) * pi * r^3. Rearranging the formula, we have r^3 = (3 * V) / (4 * pi). Taking the cube root of both sides, we get r = (3V / (4pi))^(1/3). Substituting V = 1000 cm^3 and pi ≈ 3.14159, we have r = (3 * 1000 cm^3 / (4 * 3.14159))^(1/3) ≈ (3000 / 12.56636)^(1/3) ≈ (238.732 cm^3)^(1/3) ≈ 6.33 cm (rounded to two decimal places).
4. If the volume of a sphere is multiplied by 8, the resulting volume is (8 * V) = (8 * (4/3) * pi * r^3) = (32/3) * pi * r^3. So the volume is multiplied by a factor of 32/3 or approximately 10.6667. This means that the new volume is approximately 10.6667 times the original volume.
The questions are wrong those aren't the questions
Apologies for the confusion. Can you please provide the correct questions or let me know the specific questions you need answers to?
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