# Mathematics Form 2 Measurement Questions and Answers

Mathematics Form 2 Measurement Questions and Answers.

In this online session, we are going to solve several questions on measurement.

The following sub-topics will be covered:

1. Perimeter.

2. Area.

3. Volume (Capacity).

4. Density.

5. Time.

Lessons (**38**) * SHARE*

- 1.
The two diagonals of a parallelogram are 20 cm and 28.8 cm. The acute angle between them is #62^0#. Calculate the area of the parallelogram.

2m 19s - 2.
In the figure below, ABCD is a square of side 4 cm. BXD and BYD are arcs of circles centers A and C respectively. Calculate the area of the shaded region. (Take p = 3.14)

2m 45s - 3.
A cylindrical can has a hemispherical cap. The cylinder and the hemisphere are of radius 3.5 cm. The cylindrical part is 20 cm tall. Taking p to be #22/7# calculate
(a) The area of the circular base
(b) The area of the curved cylindrical surface
(c) The area of the curve hemispherical surface
(d) The total surface area

4m 18s - 4.
A girl wanted to make a rectangular octagon of side 14 cm. She made it from a square piece of a card of size y cm by cutting off four isosceles triangles whose equal sides were x cm each, as shown in the figure below.
(a) Write down an expression for the area of the octagon in terms of x and y.
(b) Find the value of x.
(c) Find the area of the octagon.

5m 28s - 5.
Two sides of a triangle are 5 cm each and the angle between them is #120^0#. Calculate the area for the triangle.

0m 57s - 6.
A piece of wire, P cm long, is bent to form the shape shown in the figure below. The figure consists of a semicircular arc of radius r cm and two perpendicular sides of length x cm each. Express x in terms of P
and r, hence show that the area A #cm^2#, of the figure is given by #A = 1/2 pi r^2# +#1/8## ( P- pr)^2#

3m 55s - 7.
A triangular flower garden has a an area of 28 #m^2#. Two of its edges are 14 metres and 8 metres. Find the angle between the two edges.

1m 37s - 8.
The length of a solid prism is 10 cm. Its cross-section is an equilateral triangle of side 6 cm. Find the total surface area of the prism.

2m 28s - 9.
A cylindrical solid whose radius and height are equal has a surface area of 154 #cm^2#. Calculate its diameter, correct to 2 decimal places. ( Take p = 3.142)

2m 46s - 10.
In the parallelogram PQRS shown below, PQ = 8 cm and angle SPQ =# 30^0#. If the area of the parallelogram is 24 #cm^3#, find the perimeter.

1m 35s - 11.
A tailor had a piece of cloth in the shape of trapezium. The perpendicular distance between the two parallel edges was 30 cm. The lengths of the two parallel edges were 36 cm and 60 cm. The tailor cut off a semi
circular piece of the cloth of radius 14 cm from the 60 cm edge. Calculate the area of the remaining piece of cloth. ( Take p = #22/7#).

2m 9s - 12.
In the parallelogram WXYZ below, WX= 10 cm, XY = 5 cm and #angle# WXY = #150^0#.
Calculate the area of the parallelogram.

1m 24s - 13.
In the trapezium PQRS shown below, PQ = 8 cm and SR = 6 cm.
If the area of the trapezium is 28 #cm^2#, find the perpendicular distance between PQ and SR.

1m 12s - 14.
The solid shown in the figure below consists of a cylinder and a hemisphere of equal diameters of 14 cm. If the height of the solid is 22 cm, find its volume.

3m 17s - 15.
The figure below shows a vertical section of a hemispherical pot centre O. The radius OA of the pot is 20 cm. If the pot contains water to a depth of 8 cm, calculate the diameter of the water surface.

2m 14s - 16.
A metal bar 14 cm long and 5 cm in diameter is melted down and cast into circular washers. Each washer has an external diameter of 4 cm and an internal diameter of # 1 1/2# cm and is 0.3 cm thick.
Calculate the number of complete washers obtained. ( Take p =# 22/7#)

3m 56s - 17.
A room is to be constructed such that its external length and breadth are 7.5 m and 5.3 m respectively. The thickness of the wall is 15 cm, and its height is 3.3 m. A total space of 5 #m^3# is to be left out in
the walls for a door and windows.
(a) Calculate the volume of the material needed to construct the walls without the door and windows.
(b) The blocks used in constructing the
walls are 45

6m 38s - 18.
The diagram below shows a model of a cylindrical water tank. The total surface area of the model is 0.4 #m^2# and the total surface area of the actual tank is 14.4 #m^2#.
(i) If the height of the tank is 2.1 m, find the height of the model.
(ii) If the capacity of the model is 23.15 litres, find the capacity of the tank to the nearest litre.

4m 14s - 19.
A swimming pool 30 m long is 1 m deep at its shallow end and 4 m deep at its deep end. The pool is 14 m wide.
(a) Find the volume of water, in cubic metres, when the pool is full.
(b) A circular pipe of diameter 14 cm is used to empty the swimming pool. Water flows through the pipe at a rate of 5 m per second. Calculate the time it would take, to the
nearest minute, to empty the pool.

5m 57s - 20.
A rostrum is made by cutting off the upper part of a cone along a plane parallel to the base at# 2/3# up the height. What fraction of the volume of the cone does the rostrum represent?

1m 48s - 21.
A plug is made up of a hemi-spherical cap of radius 4.2 cm, and a cylinder of diameter 3.5 cm and height 5.0 cm as shown in the diagram alongside. Calculate the volume of the plug.

2m 21s - 22.
Two containers, one cylindrical and one spherical, have the same volume. The height of the cylindrical container is 50 cm and its radius is 11 cm. Find the radius of the spherical container.

2m 48s - 23.
A cylinder of radius 14 cm contains water. A metal solid cone of base radius 7 cm and height 18 cm is submerged into water. Find the change in height of the water level in the cylinder.

2m 10s - 24.
A metal bar is a hexagonal prism whose length is 30 cm. The cross-section is a regular hexagon with each side of length 6 cm. Find
(i) The area of the hexagonal face.
(ii) The volume of the metal bar.

3m 28s - 25.
A balloon, in the form of a sphere of radius 2 cm, is blown up so that the volume increases by 237.5%. Determine the new volume of the balloon in terms of p.

2m 5s - 26.
The internal and external diameters of a circular ring are 6 cm and 8 cm respectively. Find the volume of the ring if its thickness is 2 millimeters.

2m 0s - 27.
Two cylindrical containers are similar. The larger one has internal cross-section are of 45 #cm^2# and can hold 0.945 litres of liquid when full. The smaller container has internal cross-section area 20# cm^2#.
(a) Calculate the capacity of the smaller container.
(b) The larger container is filled with juice to a height of 13 cm. Juice is then drawn from it and emptied into the smaller container

8m 23s - 28.
The figure below represents a solid cone with a cylindrical hole drilled into it. The radius of the cone is 10.5 cm and its vertical height is 15 cm.
The hole has a diameter of 7 cm and depth of 8 cm.
Calculate the volume of the solid.

2m 32s - 29.
A liquid spray of mass 384 g is packed in a cylindrical container of internal radius 3.2 cm. Given that the density of the liquid is #0.6 gcm^-3#, calculate to 2 decimal places the height of the liquid in the container.

1m 55s - 30.
The density of a substance A is given as 13.6 #gcm^-3# and that of a substance B as 11.3 #gcm^-3#. Determine, correct to one decimal place, the volume of B that would have the same mass as 50 #cm^3# of A.

1m 20s - 31.
To fence one side of his farm, a farmer requires 25 posts placed 4 m apart. How many posts would he require if the posts were 3 m apart?

0m 55s - 32.
A wire of length 21 cm is bent to form the shape shown in the figure below. ABCD is a rectangle and AEB is an equilateral triangle. If the length AD of the rectangle is # 1 1/2# times its
width, calculate the width of the rectangle.

2m 58s - 33.
The diagonal of a rectangular garden measures # 11 1/4# m while its width measures #6 3/4# m. Calculate the perimeter of the garden.

2m 22s - 34.
A minor arc of a circle subtends an angle of #105^0# at the centre of the circle. If the radius of the circle is 8.4 cm, find the length of the major arc. ( Take p = #22/7#)

1m 43s - 35.
OAB is a sector of a circle of radius r cm. Angle AOB =# 60^0#. Find, in its simplest form, an expression in terms of r and p for the perimeter of the sector.
A

1m 28s - 36.
A watch which loses a half-minute every hour was set to read the correct time at 05 45 h on Monday. Determine the time, in the 12 hour system, the watch will show on the following Friday at 19 45 h.

2m 57s - 37.
Chelimo’s clock loses 15 seconds every hour. She sets the correct time on the clock at 0700h on a Monday. Determine the time shown on the clock when the correct time was 1900h on
Wednesday the same week.

2m 0s - 38.
A bus plies between two towns P and R via town Q daily. On each day it departs from P at 8.15 a.m. and stops for 40 minutes at Q before proceeding to R. On a certain day, the bus took 5 hours 40 minutes to travel from
P to Q and 3 hours 15 minutes to travel from Q to R. Find, in 24 hour clock system, the time the bus arrived at R.

1m 55s

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