Unit conversion practice problems - page 93 of 120
The International System of Units (SI) is the standard system of units used in most countries around the world. It is based on seven base units: the meter for length, the kilogram for mass, the second for time, the ampere for electric current, the kelvin for temperature, the mole for amount of substance, and the candela for luminous intensity. These units can be converted to other units using conversion factors, such as the relationship between meters and centimeters (1 meter = 100 centimeters). Other common SI unit conversions include:1 liter = 1000 milliliters
1 gram = 1000 milligrams
1 joule = 1 watt-second
1 newton = 1 kilogram-meter per second squared
In the SI system, units can be multiplied or divided by powers of ten to create larger or smaller units. These multiples are called prefixes. The most common prefixes and their meanings are:
mega- (M) = 1,000,000 (e.g. 1 megahertz = 1,000,000 hertz)
kilo- (k) = 1000 (e.g. 1 kilogram = 1000 grams)
centi- (c) = 0.01 (e.g. 1 centimeter = 0.01 meters)
milli- (m) = 0.001 (e.g. 1 milliliter = 0.001 liters)
micro- (µ) = 0.000001 (e.g. 1 microgram = 0.000001 grams)
nano- (n) = 0.000000001 (e.g. 1 nanosecond = 0.000000001 seconds)
It is important to note that, when using these prefixes, the prefix should be written before the unit symbol.
Number of problems found: 2389
- Ladder slope
What is the slope of a ladder 6.2 m long and 5.12 m in height?
- Aquarium
Find how many dm² of glass we need to make a block-shaped aquarium (the top is not covered) if the dimensions are to be a width of 50 cm, length of 120 cm, and height of 8.5 dm.
- Dimensions 16493
How many square meters of material is needed to make two identical blocks with dimensions of 6 dm, 8 dm, and 12 dm if we count 8% of the material for folds? (Round to two decimal places. )
- Rainwater 2770
The garden tank for rainwater is cuboid in shape, the bottom of which is square, with a side 150 cm long and 80 cm high. How many 15-liter buckets do we need to drain the water from the tank?
- Sine theorem 2
From the sine theorem, find the ratio of the sides of a triangle whose angles are 30°, 60°, and 90°.
- The concrete basement
The concrete base has a square base a = 90 cm and is 0.2 m high. How many kg of concrete did we use to build it if the concrete density is ρ=2200 kg/m³?
- Empty aquarium
How much does an empty aquarium weigh with dimensions: length = 40 cm, width = 30 cm, height = 20 cm, if 1 dm² of glass weighs 300 g? Calculate its weight in kilograms.
- The pool
The pool is 25 meters long, 10 meters wide, and 1.5 meters deep. How many liters are needed to fill it completely? How much will the new floor and wall paneling cost if one m² costs 10 euros?
- Metal sheet
The box has the shape of a cube with an edge length of 50 cm. How much m² of sheet metal is needed to beat a box if we add 20% on the folds of the lid and walls?
- Angles
The outer angle of the triangle ABC at vertex A is 147°12'. The outer angle at vertex B is 113°42'. What size is the internal angle at vertex C?
- Calculate 8039
Peter built a cube in Ostrava, each wall with a unique QR code. The edge of the cube is 107 cm long. Calculate how large an area its author had to cover with white and black.
- Trapezoid 36701
The field between the two parallel roads is shaped like a trapezoid with 180m and 100m long bases. The distance between the roads is 80m. When the yield of this type of cereal is 8.5 tons from 1 hectare, how many tons of barley were harvested in the field
- Descent of road
The road sign informs us the gradient is 10.9%. Calculate the angle at which the average decreases.
- Windows
Calculate the masonry area to build a wall with dimensions of 18 m × 5 m with 3 windows of size 51 cm × 51 cm.
- Aluminum cylinder
The aluminum cylinder weighs 1400 g and is 26 cm high. Its density is 2700 kg/m³. Calculate the base area of the cylinder and express the result in cm².
- Hemisphere - roof
The shape of the observatory dome is close to the hemisphere. Its outer diameter is 11 m. How many kilograms of paint and how many liters of thinner are used for its double coat if you know that 1 kg of paint diluted with 1 deciliter of thinner will paint
- Reservoir 43821
The reservoir has the shape of a sphere with a diameter of 14 m. a) How many hectoliters (hl) of water can it hold? b) How many kg of paint is needed to paint the reservoir if it is painted three times and one kg of paint is enough to paint about 9 m²?
- Specified 43301
The water tank has the shape of a block. The bottom of the tank is square, with a side length of 3 m. There are 22,500 liters of water in the tank. To what height in meters does the water in the tank reach the specified amount?
- Block-shaped 32591
Štěpán painted a block-shaped steel board measuring 2.2 m, 1.5 m, and 1.6 m twice with a protective coating. How many kilograms of paint would he consume if he used 120g of paint per 1m²?
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