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Mensuration and Trigonometry

Quick questions on Volume and surface area of solids explained: O-Level E-Maths

9short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are cones?
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A cone has volume one third of the cylinder with the same base and height:
What are pyramids?
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A pyramid's volume is one third of the base area times the vertical height:
What are spheres?
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$Vsphere=43πr3,surface area=4πr2V_{\text{sphere}} = \frac{4}{3}\pi r^3, \qquad \text{surface area} = 4\pi r^2$
What are composite solids?
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Combine solids by adding volumes, or hollow one out by subtracting. For surface area, count only the faces actually on the outside, since joined faces are hidden.
What is wrong power of r for a sphere?
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Volume uses r3r^3 and surface area uses r2r^2; do not swap them.
What are mismatched units?
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Volume is in cubic units and surface area in square units; convert lengths first.
What is q1?
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Find the volume of a cube of side 5 cm5\ \text{cm}. [1 mark]
What is q2?
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Find the volume of a cone with radius 3 cm3\ \text{cm} and height 9 cm9\ \text{cm}, taking π=3.142\pi = 3.142. [2 marks]
What is q3?
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A cone has radius 5 cm5\ \text{cm} and vertical height 12 cm12\ \text{cm}. Find its slant height. [2 marks]

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