ABCDEFGH is a cuboid.
AB = 7.3 cm
CH = 8.1 cm
Angle BCA = 48°
Find the size of the angle between AH and the plane ABCD.
Give your answer correct to 1 decimal place.
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ABCDEFGH is a cuboid.
AB = 7.3 cm
CH = 8.1 cm
Angle BCA = 48°
Find the size of the angle between AH and the plane ABCD.
Give your answer correct to 1 decimal place.
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is a horizontal rectangular field.
A vertical pole, , is placed at the corner A of the field.
Calculate the size of the angle between and the plane
Give your answer correct to one decimal place.
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The diagram shows a cuboid .
and
Work out the size of the angle between and the plane .
Give your answer correct to 3 significant figures.
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The diagram shows a triangular prism.
and.
Angle = angle = angle
Work out the size of the angle between the line and the plane .
Give your answer correct to 1 decimal place.
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The diagram shows cuboid
For this cuboid
the length of : the length of : the length of = 4 : 2 : 3
Calculate the size of the angle between and the plane .
Give your answer correct to one decimal place.
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Here is a cube with edge length cm
One diagonal is shown.
Circle the length, in centimetres, of the diagonal.
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The length of a diagonal of a cuboid is 20 cm
The diagonal makes an angle of 24° with the base.
The area of the base is 150 cm2
Work out the volume of the cuboid.
...................................... cm3
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The diagram shows a right-angled triangular prism ABCDEF.
Length AD = 11 cm, length CD = 10 cm and length CF = 6 cm.
Calculate the exact length of AF.
..................................................... cm
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The diagram shows a cuboid .
The angle between the line and the base of the cuboid is .
Calculate .
........................................... cm
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ABCDEFGH is a cuboid.
AB = 8 cm, BC = 5 cm and CG = 11 cm.
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The diagram shows a cuboid.
= 8 cm, = 4 cm and = 5 cm.
Calculate the angle between the diagonal and the plane .
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The diagram shows a cuboid .
Calculate the volume of the cuboid.
Give your answer correct to significant figures.
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Here is a cube .
is the midpoint of the edge .
Find the size of the angle between the line and the plane .
Give your answer correct to decimal place.
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is an isosceles triangle in a horizontal plane.
The point is vertically above .
Angle
is the midpoint of .
Calculate the size of the angle between and the horizontal plane .
Give your answer correct to one decimal place.
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The diagram shows cuboid
The size of the angle between and the plane is
Calculate the volume of the cuboid.
Give your answer correct to significant figures.
..............................................
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The diagram shows a triangular prism with a horizontal base .
Calculate the size of the angle between and the base .
Give your answer correct to 3 significant figures.
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The diagram shows a prism with a horizontal base.
The base of the prism, , is a square of side
Trapezium is a cross section of the prism where and are vertical edges.
Work out the size of the angle between and the base
Give your answer correct to one decimal place.
Work out the length of
Give your answer correct to one decimal place.
.............................................. cm
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is a triangular prism which represents part of a hill.
is the horizontal rectangular base.
is vertically above .
Work out the height .
..........................m
Jamil walks in a straight line from to .
Work out the size of angle .
You must show your working.
........................degrees
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Rectangle is the horizontal base of a triangular prism
is vertically above M, the midpoint of .
cm cm cm
Show that cm
Work out the size of angle
...........................degrees
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Right-angled triangleis the cross section of a prism.
is the midpoint of .
Work out the volume of the prism.
......................................cm3
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The diagram shows a cuboid ABCDEFGH.
Calculate angle BHF.
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The length of the longest diagonal of a cube is 25cm.
Calculate the total surface area of the cube.
................................................... cm2
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The diagram shows a right-angled triangular prism ABCDEF.
Calculate angle AFB.
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is a solid pyramid.
is a square of side 20 cm.
The angle between any sloping edge and the plane is 55°
Calculate the surface area of the pyramid.
Give your answer correct to 2 significant figures.
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The diagram shows the prism with cross section triangle .
Angle = 40° and angle is obtuse.
= 6 cm and = 13cm
The area of triangle is 22
Calculate the length of .
Give your answer correct to one decimal place.
..................
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The diagram shows a triangular prism.
The base, , of the prism is a square of side length 15 cm.
Angle and angle are right angles.
Angle = 35°
is the point on such that
Calculate the size of the angle between and the base of the prism.
Give your answer correct to 1 decimal place.
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The diagram shows a solid prism .
The trapezium , in which is parallel to , is a cross section of the prism.
The base of the prism is a horizontal plane.
and are rectangles.
The midpoint of is vertically above the midpoint of so that .
The perpendicular distance between edges and is 20 .
Calculate the size of the angle between and the plane .
Give your answer correct to one decimal place.
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The diagram shows the prism with horizontal base
is a cross section of the prism where
is a square
is an equilateral triangle
is the midpoint of so that is vertical.
Angle
Given that
find the value of, giving your answer in the form where and are integers.
= ...........................
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The diagram shows a solid pyramid with a horizontal base.
The base, , of the pyramid is a square of side 10 .
The vertex of the pyramid is vertically above the centre of the base so that
The total surface area of the pyramid is 360
Work out the size of the angle between and the base .
Give your answer correct to 3 significant figures.
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Alvin has a crate in the shape of a cuboid.
The crate is open at the top.
The internal dimensions of the crate are 46cm long by 46cm wide by 55cm high.
Alvin has a stick of length 95cm.
Alvin places the stick in the crate so that the shortest possible length extends out above the top of the crate.
Calculate the length of the stick that extends out of the crate.
..................................................... cm
Calculate the angle the stick makes with the base of the crate.
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The diagram shows a pyramid with a square base ABCD of side length 8cm.
The diagonals of the square, AC and BD, intersect at M.
V is vertically above M and VM = 10 cm.
Calculate the angle between VA and the base.
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The diagram shows a prism with a rectangular base, ABFE.
The cross-section, ABCD, is a trapezium with AD = BC.
AB = 8 cm, GH = 5 cm, BF = 12 cm and angle ABC = 70°.
The perpendicular from G onto EF meets EF at X.
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ABCDEFGH is a cuboid.
AB = 8 cm, BC = 5 cm and CG = 11 cm.
Ivana has a pencil of length 13cm.
Does this pencil fit completely inside the cuboid?
Show how you decide.
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The diagram shows a pyramid with a square base ABCD.
DB = 8 cm.
P is vertically above the centre, X, of the base and PX = 5 cm.
Calculate the angle between PB and the base ABCD.
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