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3d Figures

The document contains various geometry problems involving cuboids, pyramids, and prisms, focusing on calculating angles, lengths, and surface areas. It includes specific measurements and asks for calculations related to symmetry, heights, and angles in three-dimensional shapes. Each problem is structured to require mathematical reasoning and application of geometric principles.

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Hassan Hussain
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48 views5 pages

3d Figures

The document contains various geometry problems involving cuboids, pyramids, and prisms, focusing on calculating angles, lengths, and surface areas. It includes specific measurements and asks for calculations related to symmetry, heights, and angles in three-dimensional shapes. Each problem is structured to require mathematical reasoning and application of geometric principles.

Uploaded by

Hassan Hussain
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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The diagram shows a cuboid. AB = 8 cm, BC = 4 cm and CR = 5 cm.

(i) Write down the number of planes of symmetry of this cuboid. [1]
(ii) Calculate the angle between the diagonal AR and the plane BCRQ. [4]

ABCDEFGH is a cuboid.
AB = 4 cm, BC = 3 cm and AG = 12 cm.
Calculate the angle that AG makes with the base ABCD. [4]
The diagram shows a pyramid on a square base ABCD with diagonals, AC and BD, of length 8
cm.
AC and BD meet at M and the vertex, P, of the pyramid is vertically above M.
The sloping edges of the pyramid are of length 6 cm.
Calculate
(a) the perpendicular height, PM, of the pyramid, [3]
(b) the angle between a sloping edge and the base of the pyramid.[3]
The diagram shows a solid pyramid on a square horizontal base ABCD.
The diagonals AC and BD intersect at M.
P is vertically above M.
AB = 20 cm and PM = 8 cm.
a) the length of PB [4]
b) the angle between the AP and the base [2]
b) Calculate the total surface area of the pyramid. [5]

A cuboid has length 45 cm, width 22 cm and height 12 cm.


a) Calculate the length of the straight line XY. [4]
b) the angle between the XY and the base
The diagram shows a cuboid.
HD = 3 cm, EH = 5 cm and EF = 7 cm.
Calculate
(a) the length CE, [4]
(b) the angle between CE and the base CDHG. [3]

B
C

A
D

The diagram shows a prism with length 18cm and volume 253.8 cm3.
The cross-section of the prism is a right-angled triangle with base 6 cm and height h cm.
(a) (i) Show that the value of h is 4.7 . [3]
(ii) Calculate the value of x. [2]
b) the angle between AF and the base ABCD [4]
(b) Calculate the total surface area of the prism. [6]

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