The diagram shows a solid cone with radius $$\(7.6 \mathrm{~cm}\)$$ and height $$\(16 \mathrm{~cm}\)$$. A cut is made parallel to the base of the cone and the top section is removed. The remaining solid has height $$\(12 \mathrm{~cm}\)$$, as shown in the diagram. Calculate the volume of the remaining solid. [The volume, $$\(V\)$$, of a cone with radius $$\(r\)$$ and height $$\(h\)$$ is $$\(V=\frac{1}{3} \pi r^{2} h\)$$.] ...................................... $$\(\mathrm{cm}^{3}\)$$

Mathematics
IGCSE&ALevel
CAIE
Exam No:0580_s21_qp_41 Year:2021 Question No:3(b)

Answer:

953 or \(952.6\) to \(952.8\)

Knowledge points:

E5.4.1 Carry out calculations involving the surface area and volume of a cuboid, prism and cylinder. (Answers may be asked for in multiples of π.)
E5.4.2 Carry out calculations involving the surface area and volume of a sphere, pyramid and cone. (Formulae will be given for the surface area and volume of the sphere, pyramid and cone in the question.)

Solution:

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