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Volume and Surface Area of Prisms and Cylinders

Secondary 1 practice

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Volume and Surface Area of Prisms and Cylinders practice questions

Secondary 1 topics, the foundation the O-Level Mathematics 4052 syllabus builds on. 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 Prisms and Cylinders free

What this topic covers

Worked examples

Example 1

The volume of a cuboid is 450450 cm³. Its length is 1010 cm and breadth is 55 cm. Find the height.
10 cm5 cmhNot drawn to scale
Show the worked solution
  • V=l×b×hV = l \times b \times h
  • 450=10×5×h450 = 10 \times 5 \times h
  • 450=50×h450 = 50 \times h
  • h=45050h = \frac{450}{50}
  • =9= 9 cm

Answer: 99

Example 2

A triangular prism has a right-triangular cross-section with sides 8 cm, 15 cm and 17 cm, the right angle being between the first two. The length of the prism is 16 cm. Find its total surface area.
8 cm16 cm15 cmNot drawn to scale
Show the worked solution
  • Area of triangular face=12×8×15\text{Area of triangular face} = \frac{1}{2} \times 8 \times 15
  • =60= 60 cm²
  • Surface area=2×triangular face+3×rectangular faces\text{Surface area} = 2 \times \text{triangular face} + 3 \times \text{rectangular faces}
  • =2×60+8×16+15×16+17×16= 2 \times 60 + 8 \times 16 + 15 \times 16 + 17 \times 16
  • =120+(8+15+17)×16= 120 + (8 + 15 + 17) \times 16
  • =120+40×16= 120 + 40 \times 16
  • =120+640= 120 + 640
  • =760= 760 cm²

Answer: 760760

Example 3

A cylinder has volume 117π117\pi cm³ and radius 33 cm. Find the height.
Show the worked solution
  • V=πr2hV = \pi r^2 h
  • 117π=π×32×h117\pi = \pi \times 3^2 \times h
  • 117=9×hdivide both sides by π117 = 9 \times h \quad \scriptsize\textit{divide both sides by } \pi
  • h=1179h = \frac{117}{9}
  • =13= 13 cm

Answer: 1313

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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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