a globe of the earth measures 12 inches in a diameter. calculate the surface area and volume of this globe
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To calculate the surface area and volume of a globe, you need to use the formulas specific to spheres.
1. Surface Area:
The surface area of a sphere can be calculated using the formula:
Surface Area = 4πr²
In this case, the diameter of the globe is given as 12 inches. To find the radius, divide the diameter by 2:
Radius = Diameter / 2 = 12 inches / 2 = 6 inches
Plug the value of the radius into the surface area formula:
Surface Area = 4π(6 inches)²
Now, calculate the surface area using the value of π (pi) as 3.14159:
Surface Area = 4 * 3.14159 * (6 inches)²
Surface Area ≈ 4 * 3.14159 * 36 square inches
Surface Area ≈ 452.389 square inches
Therefore, the surface area of the globe is approximately 452.389 square inches.
2. Volume:
The volume of a sphere can be calculated using the formula:
Volume = (4/3)πr³
Using the given radius value of 6 inches, plug it into the volume formula:
Volume = (4/3)π(6 inches)³
Now, calculate the volume using the value of π (pi) as 3.14159:
Volume = (4/3) * 3.14159 * (6 inches)³
Volume ≈ (4/3) * 3.14159 * 216 cubic inches
Volume ≈ 904.779 cubic inches
Therefore, the volume of the globe is approximately 904.779 cubic inches.