3d Pythagoras and Trigonometry worksheet
8 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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5 marks
A carton is in the shape of a cuboid measuring \(18\) cm by \(21\) cm by \(30\) cm.
(a)Find the length of the longest straight rod that will fit inside the carton.
Give your answer to 1 decimal place.
(b)A straight drinking straw is \(40\) cm long.
Will the drinking straw fit inside the carton? Write Yes or No.
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3 marks
Here is a cuboid.
Its base is a rectangle measuring \(7\) cm by \(14\) cm, and its height is \(h\) cm.
The distance from one corner of the cuboid to the opposite corner is \(27\) cm.
Work out the value of \(h\).
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4 marks
Here is a cuboid \(ABCDEFGH\).
\(AB = 7\) cm, \(AD = 11\) cm and \(BF = 16\) cm.
Work out the size of the angle between \(AG\) and the base \(ABCD\).
Give your answer correct to 1 decimal place.
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7 marks
The diagram shows a solid pyramid \(ABCDV\).
The base \(ABCD\) is a square of side \(18\) cm. The vertex \(V\) is vertically above the centre of the base, and the perpendicular height of the pyramid is \(19\) cm.
All four sloping edges are the same length. One of them is marked \(x\).
(a)Work out the value of \(x\).
Give your answer to 1 decimal place.
(b)Work out the size of the angle between the edge marked \(x\) and the base \(ABCD\).
Give your answer to the nearest degree.
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5 marks
A container is in the shape of a cuboid measuring \(20\) cm by \(18\) cm by \(23\) cm.
(a)Find the length of the longest straight rod that will fit inside the container.
Give your answer to 1 decimal place.
(b)A straight bamboo cane is \(40\) cm long.
Will the bamboo cane fit inside the container? Write Yes or No.
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3 marks
Here is a cuboid.
Its base is a rectangle measuring \(15\) cm by \(18\) cm, and its height is \(h\) cm.
The distance from one corner of the cuboid to the opposite corner is \(35\) cm.
Find the value of \(h\).
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4 marks
The diagram shows a cuboid \(ABCDEFGH\).
\(AB = 14\) cm, \(AD = 6\) cm and \(BF = 15\) cm.
Work out the size of the angle between \(AG\) and the base \(ABCD\).
Give your answer correct to 1 decimal place.
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7 marks
Here is a solid pyramid \(ABCDV\).
The base \(ABCD\) is a square of side \(10\) cm. The vertex \(V\) is vertically above the centre of the base, and the perpendicular height of the pyramid is \(16\) cm.
All four sloping edges are the same length. One of them is marked \(x\).
(a)Find the value of \(x\).
Give your answer to 1 decimal place.
(b)Find the size of the angle between the edge marked \(x\) and the base \(ABCD\).
Give your answer to the nearest degree.
Answers
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(a) \(40.8\ \text{cm}\)
(b) Yes - \(22\ \text{cm}\)
- \(50.8^\circ\)
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(a) \(22.9\ \text{cm}\)
(b) \(56^\circ\) -
(a) \(35.4\ \text{cm}\)
(b) No - \(26\ \text{cm}\)
- \(44.6^\circ\)
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(a) \(17.5\ \text{cm}\)
(b) \(66^\circ\)