Unit conversion practice problems - page 118 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: 2387
- Metal tube
Calculate the metal tube mass 8 dm long with an outer radius of 5cm and an inner radius of 4.5cm. One cm³ of this metal is 9.5g.
- Quadrilateral pyramid
The height of a regular quadrilateral pyramid is 6.5 cm, and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body—round calculations to 1 decimal place.
- Forces
Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?
- The coil
How many ropes (a diameter of 8 mm) fit on the coil (threads are wrapped close together)? The coil has the following dimensions: The inner diameter is 400mm. The outside diameter is 800mm. The length of the coil is 470mm.
- Glass
How many glasses are needed to produce glass with a base of a regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?
- Quadrilateral 25201
Calculate the volume and surface of a regular quadrilateral prism with a base edge a = 46 mm and a height v = 0.67 dm.
- Heptagonal pyramid
A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm, and the upper base is 14 cm. The altitude is 30 cm. Determine the weight in kg if the wood density is 10 grams/cm³.
- The quadrilateral pyramid
The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.
- Ground 8370
The arch has a radius of 3.3 m, a span of 3.25 m, and a height of 20 cm above the ground. What is the length of the arc to reach the ground?
- Quadrilateral 81097
The quadrilateral ABCD is symmetrical about the diagonal AC. The length of AC is 12 cm, the length of BC is 6 cm, and the interior angle at vertex B is right. points E and F are given on the sides AB, and AD so that the triangle ECF is equilateral. Determ
- Subtended 83194
A circle k with a center at point S and a radius of 6 cm is given. Calculate the size of the central angle subtended by a chord 10 cm long.
- Tetrahedral pyramid
Calculate the regular tetrahedral pyramid's volume and surface if the area of the base is 20 cm² and the deviation angle of the side edges from the plane of the base is 60 degrees.
- Quadrilateral 82146
Calculate the volume and surface area of a regular quadrilateral prism with base edge a=24 cm if the body diagonal makes an angle of 66° with the base.
- Corresponding 6021
How much paint do we need to paint a pool in the shape of a 6-sided prism? The base edge measures 21 dm, the corresponding height is 1.8 m, and the pool height is 150 cm. We need 0.21 kg of paint per 1 m².
- Goat and circles
What is the radius of a circle centered on the other circle, and is the intersection of the two circles equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which
- Prism-shaped 6137
The prism-shaped vessel with a rhomboid base has one base diagonal of 10 cm and the edge of the base 14 cm. The edge of the base and the prism height are in a ratio of 2:5. How many liters of water is in the container when it is filled to four-fifths of t
- Two forces
The two forces, F1 = 580N and F2 = 630N, have an angle of 59 degrees. Calculate their resultant force, F.
- Establish 72234
How many kg of grass seed should be bought to establish a lawn around a circular fountain with a diameter of 5 m if the lawn is to be 1.5 m wide and 1 g of grass seed is used per 1 dm of the square area?
- Truncated pyramid
The concrete pedestal in a regular quadrilateral truncated pyramid has a height of 12 cm; the pedestal edges have lengths of 2.4 and 1.6 dm. Calculate the surface of the base.
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