Social networks

OpenProf

Unlock access to content

Select one option:

Free of charge

Unlock the chapter "Conversion of Rates and Measurement"

Unlock access to the solution of problems in this chapter.
Free of charge Price: 3 £

Continue »

Subscribe to OpenProf If you do not get a better grade, you get your money back!

Unlock access to all problems solutions.
Available from 8.25 £ / month.

Continue »

Solved problems for the chapter:

Conversion of Rates and Measurement

View the theory »

Measurement and convert rates for KS4

1. Measuring length (distance)

2. The measurement of area

3. Volume measurement

4. Measurement of (plane) angles

4.1. Measuring angles in angular degrees

4.2. Measuring angles in radians

4.3. Conversion between angular degrees and radians

4.3.1. Unit circle

5. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:conversion_of_rates_and_measurement/3565/

Example 1.

Convert the length: 3 m 3 cm 70 mm to decimeters.

Example 2.

Convert:

3 m 57 dm 4 mm to centimetres.

Convert the given area to square decimetres:

Convert the given area to square centimetres:

5 944 816

Express the given angle in the form of degrees, minutes and seconds:

Converts the given angle to degrees:

The following angle is given:

Subtract the half of the complementary angle of from its complementary angle.

Name the new angle, .

Given that the angles and are supplementary, and that the angles and are complementary. If is three times larger than the angle , calculate the values of , and .

The difference between three times the angle and two times the angle represents a right angle, and the sum of two times the value of the angle and the three times the value of the angle is supplementary. Find the measure of the angles and to the nearest angular second.

10.

The angle measures 45% of the sum of angles on a straight line. How many times larger is to its complementary angle? Also, calculate the complementary and supplementary of the angle .

11.

Given two supplementary angles and in the ratio 5:7, find the measures of these angles.

12.

Given the diagram above with , determine the value of angles , and .

13.

Calculate the area of the shaded region in the diagram below to one decimal place.

14.

A rectangle with sides of 10 cm and 4 cm is folded to form a cylinder.

Draw the sketch and calculate the area of the resulting cylinder to the nearest .
Calculate the length of the longest rigid rod that could still be hidden in this cylinder.
How much angle does this rod enclose with the base surface of the cylinder? As indicated in the sketch.

15.

A sheet of paper has the shape of a rectangle with a length of 30 cm and a width of 20 cm.

Roll the sheet into a cylinder so that the shorter side is the height of the cylinder. Calculate the area of the resulting cylinder.
Let the sheet be transformed into a regular 4-sided prism with a height equal to the length of the shorter side. Calculate the surface area of the prism.
By what percentage is the area of the cylinder larger than the area of the prism?