NOT TO SCALE The diagram shows a pyramid with a square base $$$B C D E$$$. The diagonals $$$C E$$$ and $$$B D$$$ intersect at $$$M$$$, and the vertex $$$F$$$ is directly above $$$M$$$. $$$B E=12 \mathrm{~cm}$$$ and $$$F M=9 \mathrm{~cm}$$$. (i) Calculate the volume of the pyramid. [The volume, $$$V$$$, of a pyramid with base area $$$A$$$ and height $$$h$$$ is $$$V=\frac{1}{3} A h$$$.] ..................................... $$$\mathrm{cm}^{3}$$$ (ii) Calculate the total surface area of the pyramid. ..................................... $$$\mathrm{cm}^{2}$$$

Mathematics

IGCSE&ALevel

CAIE

Exam No：0580_m24_qp_42 Year：2024 Question No：4(a)

Answer:

Knowledge points:

E4.7.1 angles at a point

E4.7.10 angles in the same segment are equal

E4.7.11 angles in opposite segments are supplementary; cyclic quadrilaterals

E4.7.12 alternate segment theorem.

E4.7.2 angles at a point on a straight line and intersecting straight lines

E4.7.3 angles formed within parallel lines

E4.7.4 angle properties of triangles and quadrilaterals

E4.7.5 angle properties of regular polygons

E4.7.6 angle in a semicircle

E4.7.7 angle between tangent and radius of a circle

E4.7.8 angle properties of irregular polygons

E4.7.9 angle at the centre of a circle is twice the angle at the circumference

E5.2 Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium and compound shapes derived from these.

Answer:

Knowledge points:

Solution:

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