DP Mathematical Studies Questionbank
5.4
Description
[N/A]Directly related questions
- 18M.2.sl.TZ1.6d: Show that the volume, V cm3 , of the new trash can is given by \(V = 110\pi {r^3}\).
- 18M.1.sl.TZ1.14c: Calculate the curved surface area of the remaining solid.
- 18M.1.sl.TZ1.14b: Calculate the curved surface area of the cone which has been removed.
- 18M.1.sl.TZ1.14a: Calculate the radius of the base of the cone which has been removed.
- 16M.2.sl.TZ2.4f: Calculate the maximum number of cups that can be completely filled with the...
- 16M.2.sl.TZ2.4e: Chavi is celebrating her birthday with her friends on the playground. Her mother brings a...
- 16M.2.sl.TZ2.4d: Chavi estimates that the height of the tree is \(6\,{\text{m}}\). Calculate the percentage error...
- 16M.2.sl.TZ2.4c: There is a tree at \({\text{C}}\), perpendicular to the ground. The angle of elevation to the top...
- 16M.2.sl.TZ2.4b: Calculate angle \({\text{ADC}}\).
- 16M.2.sl.TZ2.4a: A playground, when viewed from above, is shaped like a quadrilateral, \({\text{ABCD}}\),...
- 16M.1.sl.TZ2.11c: Dan is going to paint the curved surface and the base of the snack container. Calculate the area...
- 16M.1.sl.TZ2.11b: Calculate the area of the base of the container.
- 16M.1.sl.TZ2.11a: A snack container has a cylindrical shape. The diameter of the base is \(7.84\,{\text{cm}}\). The...
- 16M.1.sl.TZ2.1b: The surface area of the Earth that is covered by water is approximately...
- 16M.1.sl.TZ2.1a: Assume that the Earth is a sphere with a radius, \(r\) , of \(6.38 \times {10^3}\,{\text{km}}\)...
- 16M.2.sl.TZ1.4f: Ahmad and his friends like to sit in the pyramid’s shadow, \({\text{ABW}}\), to cool down.At...
- 16M.2.sl.TZ1.4e: Ahmad is a tour guide at the Great Pyramid of Giza. He claims that the amount of stone used to...
- 16M.2.sl.TZ1.4d: Write down your answer to part (c) in the form \(a \times {10^k}\) where...
- 16M.2.sl.TZ1.4c: Find the volume of the pyramid.
- 16M.2.sl.TZ1.4b: Calculate the height of the pyramid, \({\text{VO}}\) .
- 16M.2.sl.TZ1.4a: The Great Pyramid of Giza in Egypt is a right pyramid with a square base. The pyramid is made of...
- 16N.1.sl.TZ0.11b: Calculate the angle of depression from A to B.
- 16N.1.sl.TZ0.11a: Calculate CD, the height of the observation deck above the ground.
- 10M.1.sl.TZ1.1a: Calculate the exact volume of the container. Give your answer as a fraction.
- 10M.1.sl.TZ2.14b: Calculate the length of AF.
- 10M.1.sl.TZ2.14c: Find the size of the angle between AF and AG.
- 10M.2.sl.TZ1.4a.i: Write down the length of VA in metres.
- 11N.1.sl.TZ0.9a: Calculate the volume of the observatory.
- 11N.1.sl.TZ0.9b: The hemispherical roof is to be painted. Calculate the area that is to be painted.
- 12N.1.sl.TZ0.12b: M is the midpoint of EF . Calculate the length of BM .
- 12N.1.sl.TZ0.12c: M is the midpoint of EF . Find the size of the angle between BM and the face ADEF .
- 10M.2.sl.TZ2.5a: Show that \(h = \frac{{600}}{{\pi {x^2}}}\).
- 12M.2.sl.TZ2.4d: Show that the angle between the line VM and the base of the pyramid is 52° correct to 2...
- 09N.2.sl.TZ0.1A, c: Calculate the angle between VM and ABCD.
- 09N.2.sl.TZ0.1A, a: Write down the length of XM.
- 11M.1.sl.TZ1.7b: Calculate the length of AG.
- 11M.1.sl.TZ1.7c: Calculate the angle that AG makes with the floor.
- 09M.2.sl.TZ1.4a, i: Write down the size of angle BAF.
- 09M.1.sl.TZ2.15a: Find the length of OB.
- 09M.1.sl.TZ2.15b: Find the size of angle OBP.
- 11M.1.sl.TZ2.8b: The cannon balls are to be melted down to form a sculpture in the shape of a cone. The base...
- 13M.2.sl.TZ1.5d: Show that the length of CQ is 50.37 m, correct to 4 significant figures.
- 13M.1.sl.TZ2.1a: Calculate the exact value of the volume of the cuboid, in cm3.
- 13M.2.sl.TZ2.3d: Calculate the total surface area of the tent, including the base.
- 13M.2.sl.TZ2.3e: Calculate the volume of the tent.
- 13M.2.sl.TZ2.3g: Calculate the angle between VM and the base of the tent.
- SPM.1.sl.TZ0.6b: Calculate the angle between VC and the base ABCD.
- SPM.1.sl.TZ0.6a: Calculate(i) the length of AC;(ii) the length of VC.
- SPM.1.sl.TZ0.12a: Calculate the length, \(l\), of the slant height of the cone.
- SPM.2.sl.TZ0.2c: Calculate the volume of the office block.
- 08N.1.sl.TZ0.12a: Calculate the length of \({\text{VM}}\).
- 08N.1.sl.TZ0.12b: Calculate the vertical height of the pyramid.
- 08M.2.sl.TZ1.4ii.a: Using the letters on the diagram draw a triangle showing the position of a \({70^ \circ }\) angle.
- 08M.2.sl.TZ2.3ii.b: \({\text{M}}\) is the midpoint of the base of one of the triangles and \({\text{O}}\) is the apex...
- SPM.2.sl.TZ1.6a: Write down an expression for \(T\) in terms of \(r\), \(l\) and \(\pi \).
- 14M.2.sl.TZ2.5a: Express the volume of the parcel in terms of \(l\) and \(w\).
- 14M.2.sl.TZ2.6g: The water tank is shown below. It is partially filled with water. The water tank has a...
- 14M.2.sl.TZ2.5c: The parcel is tied up using a length of string that fits exactly around the parcel, as shown in...
- 14M.1.sl.TZ1.8a: Calculate OV, the height of the cone.
- 14M.2.sl.TZ1.6b: The volume of the lobster trap is \(0.75{\text{ }}{{\text{m}}^{\text{3}}}\). Write down an...
- 14M.2.sl.TZ1.6a: Write down an expression for \(T\) in terms of \(r\), \(l\) and \(\pi \).
- 15M.1.sl.TZ2.8b: Find the size of angle \({\rm{C\hat MB}}\).
- 15M.1.sl.TZ1.15a: Find the value of \(a\).
- 15M.1.sl.TZ1.9a: Calculate \({\text{VM}}\).
- 15M.2.sl.TZ2.2c: Temi makes some crafts with perfume bottles, like the one above, once they are empty. Temi wants...
- 15M.2.sl.TZ2.2d: Temi covers the perfume bottles with a paint that costs 3 South African rand (ZAR) per...
- 15M.2.sl.TZ2.2a: (i) Show that the vertical height of the cone is \(2.65\) cm correct to three significant...
- 15M.2.sl.TZ2.2b: The bottle contains \({\text{125 c}}{{\text{m}}^{\text{3}}}\) of perfume. The bottle is not full...
- 14N.2.sl.TZ0.3d: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped tents...
- 14N.2.sl.TZ0.3f: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped tents...
- 17M.1.sl.TZ2.3b: Find the total length of wire needed to construct this wireframe. Give your answer in centimetres...
- 17M.1.sl.TZ2.3a: Find the length of one of the straight pieces in the wireframe.
- 14N.2.sl.TZ0.3a: Show that the slant height, \(l\), is \(5\) m, correct to the nearest metre.
- 14N.2.sl.TZ0.3b: (i) Find the circumference of the base of the cone. (ii) Find the radius, \(r\), of the...
- 14N.2.sl.TZ0.3c: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped tents...
Sub sections and their related questions
Geometry of three-dimensional solids: cuboid; right prism; right pyramid; right cone; cylinder; sphere; hemisphere; and combinations of these solids.
- 10M.1.sl.TZ1.1a: Calculate the exact volume of the container. Give your answer as a fraction.
- 10M.1.sl.TZ2.14b: Calculate the length of AF.
- 10M.2.sl.TZ1.4a.i: Write down the length of VA in metres.
- 11N.1.sl.TZ0.9a: Calculate the volume of the observatory.
- 11N.1.sl.TZ0.9b: The hemispherical roof is to be painted. Calculate the area that is to be painted.
- 12N.1.sl.TZ0.12b: M is the midpoint of EF . Calculate the length of BM .
- 10M.2.sl.TZ2.5a: Show that \(h = \frac{{600}}{{\pi {x^2}}}\).
- 09N.2.sl.TZ0.1A, a: Write down the length of XM.
- 09M.2.sl.TZ1.4a, i: Write down the size of angle BAF.
- 09M.1.sl.TZ2.15a: Find the length of OB.
- 09M.1.sl.TZ2.15b: Find the size of angle OBP.
- 11M.1.sl.TZ2.8b: The cannon balls are to be melted down to form a sculpture in the shape of a cone. The base...
- 13M.2.sl.TZ1.5d: Show that the length of CQ is 50.37 m, correct to 4 significant figures.
- 13M.1.sl.TZ2.1a: Calculate the exact value of the volume of the cuboid, in cm3.
- 13M.2.sl.TZ2.3d: Calculate the total surface area of the tent, including the base.
- 13M.2.sl.TZ2.3e: Calculate the volume of the tent.
- SPM.1.sl.TZ0.6a: Calculate(i) the length of AC;(ii) the length of VC.
- SPM.1.sl.TZ0.12a: Calculate the length, \(l\), of the slant height of the cone.
- SPM.2.sl.TZ0.2c: Calculate the volume of the office block.
- 08N.1.sl.TZ0.12b: Calculate the vertical height of the pyramid.
- 08M.2.sl.TZ1.4ii.a: Using the letters on the diagram draw a triangle showing the position of a \({70^ \circ }\) angle.
- SPM.2.sl.TZ1.6a: Write down an expression for \(T\) in terms of \(r\), \(l\) and \(\pi \).
- 14M.2.sl.TZ2.5a: Express the volume of the parcel in terms of \(l\) and \(w\).
- 14M.2.sl.TZ2.5c: The parcel is tied up using a length of string that fits exactly around the parcel, as shown in...
- 14M.2.sl.TZ2.6g: The water tank is shown below. It is partially filled with water. The water tank has a...
- 14M.1.sl.TZ1.8a: Calculate OV, the height of the cone.
- 14M.2.sl.TZ1.6a: Write down an expression for \(T\) in terms of \(r\), \(l\) and \(\pi \).
- 14M.2.sl.TZ1.6b: The volume of the lobster trap is \(0.75{\text{ }}{{\text{m}}^{\text{3}}}\). Write down an...
- 14N.2.sl.TZ0.3a: Show that the slant height, \(l\), is \(5\) m, correct to the nearest metre.
- 14N.2.sl.TZ0.3b: (i) Find the circumference of the base of the cone. (ii) Find the radius, \(r\), of the...
- 14N.2.sl.TZ0.3c: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped tents...
- 14N.2.sl.TZ0.3d: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped tents...
- 14N.2.sl.TZ0.3f: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped tents...
- 15M.1.sl.TZ1.9a: Calculate \({\text{VM}}\).
- 15M.1.sl.TZ1.15a: Find the value of \(a\).
- 15M.2.sl.TZ2.2a: (i) Show that the vertical height of the cone is \(2.65\) cm correct to three significant...
- 15M.2.sl.TZ2.2b: The bottle contains \({\text{125 c}}{{\text{m}}^{\text{3}}}\) of perfume. The bottle is not full...
- 15M.2.sl.TZ2.2c: Temi makes some crafts with perfume bottles, like the one above, once they are empty. Temi wants...
- 15M.2.sl.TZ2.2d: Temi covers the perfume bottles with a paint that costs 3 South African rand (ZAR) per...
- 18M.2.sl.TZ1.6d: Show that the volume, V cm3 , of the new trash can is given by \(V = 110\pi {r^3}\).
The distance between two points; eg between two vertices or vertices with midpoints or midpoints with midpoints.
- 11M.1.sl.TZ1.7b: Calculate the length of AG.
- 09M.1.sl.TZ2.15a: Find the length of OB.
- 08N.1.sl.TZ0.12a: Calculate the length of \({\text{VM}}\).
- 18M.2.sl.TZ1.6d: Show that the volume, V cm3 , of the new trash can is given by \(V = 110\pi {r^3}\).
The size of an angle between two lines or between a line and a plane.
- 10M.1.sl.TZ2.14c: Find the size of the angle between AF and AG.
- 12N.1.sl.TZ0.12c: M is the midpoint of EF . Find the size of the angle between BM and the face ADEF .
- 12M.2.sl.TZ2.4d: Show that the angle between the line VM and the base of the pyramid is 52° correct to 2...
- 09N.2.sl.TZ0.1A, c: Calculate the angle between VM and ABCD.
- 11M.1.sl.TZ1.7c: Calculate the angle that AG makes with the floor.
- 09M.2.sl.TZ1.4a, i: Write down the size of angle BAF.
- 09M.1.sl.TZ2.15b: Find the size of angle OBP.
- 13M.2.sl.TZ2.3g: Calculate the angle between VM and the base of the tent.
- SPM.1.sl.TZ0.6b: Calculate the angle between VC and the base ABCD.
- 08M.2.sl.TZ2.3ii.b: \({\text{M}}\) is the midpoint of the base of one of the triangles and \({\text{O}}\) is the apex...
- 15M.1.sl.TZ2.8b: Find the size of angle \({\rm{C\hat MB}}\).
- 18M.2.sl.TZ1.6d: Show that the volume, V cm3 , of the new trash can is given by \(V = 110\pi {r^3}\).
