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Volume and Surface Area of Pyramids, Cones and Spheres

Secondary 2 practice

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Volume and Surface Area 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.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise Volume and Surface Area of Pyramids, Cones and Spheres free

What this topic covers

Worked examples

Example 1

A square pyramid has a base side of 66 cm and a slant height of 66 cm. Find the total surface area of the pyramid.
Show the worked solution
  • Total surface area=base area+4×area of triangular face\text{Total surface area} = \text{base area} + 4 \times \text{area of triangular face}
  • =s2+4×12×s×l= s^2 + 4 \times \frac{1}{2} \times s \times l
  • =62+2×6×6= 6^2 + 2 \times 6 \times 6
  • =36+72= 36 + 72
  • =108= 108 cm²

Answer: 108108

Example 2

The volume of a cone is 189π189\pi cm³ and its base radius is 99 cm. Find the height of the cone.
Show the worked solution
  • V=13πr2hV = \dfrac{1}{3}\pi r^2 h
  • 189π=13×π×92×h189\pi = \dfrac{1}{3} \times \pi \times 9^2 \times h
  • 189π=813πhsimplify189\pi = \dfrac{81}{3}\pi h \quad \scriptsize\textit{simplify}
  • 189=813hdivide both sides by π189 = \dfrac{81}{3} h \quad \scriptsize\textit{divide both sides by } \pi
  • h=189×381h = \dfrac{189 \times 3}{81}
  • =56781= \dfrac{567}{81}
  • =7= 7 cm

Answer: 77

Example 3

The surface area of a sphere is 16π16\pi cm². Find the radius of the sphere.
Show the worked solution
  • SA=4πr2SA = 4\pi r^2
  • 16π=4πr216\pi = 4\pi r^2
  • 16=4r2divide both sides by π16 = 4r^2 \quad \scriptsize\textit{divide both sides by } \pi
  • r2=164r^2 = \frac{16}{4}
  • r2=4r^2 = 4
  • r=2r = 2 cm

Answer: 22

Questions parents ask

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Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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