Answer:
154m2
explanation given below
Step-by-step explanation:
Finding radius and surface area of the sphere:
1. Convert volume to cubic centimeters:
First, we need to convert the mixed fraction 179 2/3 cm³ to a whole number of cubic centimeters. We can do this by multiplying the numerator of the fraction by the denominator and adding it to the whole number:
179 2/3 cm³ = 179 cm³ + (2/3) cm³ = 179 cm³ + (0.6666 cm³) = 179.6666 cm³ (rounded to 5 decimal places)
2. Calculate radius:
We know the formula for the volume of a sphere is:
V = (4/3)πr³
where V is the volume, π is pi (approximately 3.14159), and r is the radius. We can rearrange this formula to solve for r:
r = ³√(3V / (4π))
Plugging in the volume we calculated above:
r = ³√(3 * 179.6666 cm³ / (4 * 3.14159)) ≈ 3.48 cm (rounded to 2 decimal places)
3. Calculate surface area:
The formula for the surface area of a sphere is:
SA = 4πr²
Using the radius we found:
SA = 4 * 3.14159 * (3.48 cm)² ≈ 154.16 cm² (rounded to 2 decimal places)
Therefore, the sphere has a radius of approximately 3.48 cm and a surface area of approximately 154.16 cm².
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Verified answer
Answer:
154m2
explanation given below
Step-by-step explanation:
Finding radius and surface area of the sphere:
1. Convert volume to cubic centimeters:
First, we need to convert the mixed fraction 179 2/3 cm³ to a whole number of cubic centimeters. We can do this by multiplying the numerator of the fraction by the denominator and adding it to the whole number:
179 2/3 cm³ = 179 cm³ + (2/3) cm³ = 179 cm³ + (0.6666 cm³) = 179.6666 cm³ (rounded to 5 decimal places)
2. Calculate radius:
We know the formula for the volume of a sphere is:
V = (4/3)πr³
where V is the volume, π is pi (approximately 3.14159), and r is the radius. We can rearrange this formula to solve for r:
r = ³√(3V / (4π))
Plugging in the volume we calculated above:
r = ³√(3 * 179.6666 cm³ / (4 * 3.14159)) ≈ 3.48 cm (rounded to 2 decimal places)
3. Calculate surface area:
The formula for the surface area of a sphere is:
SA = 4πr²
Using the radius we found:
SA = 4 * 3.14159 * (3.48 cm)² ≈ 154.16 cm² (rounded to 2 decimal places)
Therefore, the sphere has a radius of approximately 3.48 cm and a surface area of approximately 154.16 cm².