fundamental SI units of:
- a distance of exactly 26 miles
- an area of 1.0 square root
-the volume of a sphere of radius 1.40 picometers
-a density of 38. tons per cubic furlong
To find the fundamental SI units for the given quantities, we need to understand the relationships between different units and their conversions. The fundamental SI units are the standard units used to measure different physical quantities in the International System of Units (SI).
1. Distance of exactly 26 miles:
The SI unit for distance is the meter (m). To convert miles to meters, we can use the conversion factor: 1 mile = 1609.34 meters. Therefore, the distance of 26 miles is equal to 26 x 1609.34 = 41,841.84 meters.
Fundamental SI unit: meters (m)
2. Area of 1.0 square root:
It seems that there might be an error or a missing unit for this quantity. The square root is a mathematical operation, and it cannot be used directly as a unit for measuring area. If there's a missing unit, please provide it so we can determine the fundamental SI units.
3. Volume of a sphere with a radius of 1.40 picometers:
The SI unit for volume is the cubic meter (m³). To find the volume of a sphere, we can use the formula: V = (4/3)πr³, where r is the radius of the sphere.
Given the radius as 1.40 picometers (pm), we need to convert it to meters since SI units are in meters. 1 picometer is equal to 1 x 10^-12 meters (m). Thus, 1.40 picometers is equal to 1.40 x 10^-12 meters.
Now we can substitute r = 1.40 x 10^-12 meters into the volume formula:
V = (4/3)π(1.40 x 10^-12 m)³
≈ 10.358 x 10^-36 m³
≈ 1.04 x 10^-35 m³
Fundamental SI unit: cubic meter (m³)
4. Density of 38. tons per cubic furlong:
The SI unit for density is kilograms per cubic meter (kg/m³). We need to convert tons (imperial unit) and furlongs (non-SI unit) to kilograms and meters, respectively.
To convert tons to kilograms, we use the conversion factor: 1 ton = 907.185 kilograms.
To convert furlongs to meters, we use the conversion factor: 1 furlong = 201.168 meters.
Now we can determine the density in SI units:
Density = 38 tons / (1 furlong)³
= (38 x 907.185 kg) / (201.168 m)³
≈ 1957.98 kg / m³
Fundamental SI unit: kilograms per cubic meter (kg/m³)