Volume and SA of Pyramids, Cones and Spheres practice questions
Secondary 2 topics, working towards the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.
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correction. The worked solution is there once a genuine attempt has been made.
A square pyramid has a height of 12 cm and a volume of 64 cm³. Find the side length of its square base.
Show the worked solution
$V = \frac{1}{3} \times s^2 \times h$
$64 = \frac{1}{3} \times s^2 \times 12$
$s^2 = \frac{3 \times 64}{12}$
$= \frac{192}{12}$
$= 16$
$s = \sqrt{16}$
$= 4$ cm
Answer: 4
Example 2
A cone has base radius 30 cm and height 16 cm. Find the total surface area of the cone. Leave your answer in terms of π.
Show the worked solution
$\text{Find slant height using Pythagoras' theorem:}$
$l^2 = r^2 + h^2$
$= 30^2 + 16^2$
$= 900 + 256$
$= 1156$
$l = \sqrt{1156}$
$= 34$ cm
$\text{Total SA} = \pi r(l + r)$
Answer: 1920
Example 3
Find the volume of a solid hemisphere with radius 24 cm. Leave your answer in terms of π.
Show the worked solution
$V_{\text{hemisphere}} = \frac{2}{3}\pi r^3$
$= \frac{2}{3} \times \pi \times 24^3$
$= \frac{2}{3} \times \pi \times 13824$
$= 9216\pi$ cm³
Answer: 9216
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O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.
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