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2 answers:
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4.
The ratio is 3/4 for corresponding dimensions, the ratio of their surface areas is equal to the square of this ratio:
Simplify the exponent:
Cross multiply:
Divide 9 to both sides:
So the surface area of the second solid is 54 square meters.
The ratio is 3/4 for corresponding dimensions, the ratio of their volumes is equal to the cube of this ratio:
Simplify the exponent:
Cross multiply:
Divide 64 to both sides:
5.
A globe is a sphere, use the formula for the volume of a sphere:
The radius is half of the diameter, so the radius here is 40/2 = 20. Plug it in the formula, use 3.14 to approximate for Pi:
Simplify the exponent:
Multiply:
The ratio is 3/4 for corresponding dimensions, the ratio of their surface areas is equal to the square of this ratio:
Simplify the exponent:
Cross multiply:
Divide 9 to both sides:
So the surface area of the second solid is 54 square meters.
The ratio is 3/4 for corresponding dimensions, the ratio of their volumes is equal to the cube of this ratio:
Simplify the exponent:
Cross multiply:
Divide 64 to both sides:
5.
A globe is a sphere, use the formula for the volume of a sphere:
The radius is half of the diameter, so the radius here is 40/2 = 20. Plug it in the formula, use 3.14 to approximate for Pi:
Simplify the exponent:
Multiply: