Coaching Centre
Volume of prisms and cylinders
Volume as area of cross-section times height for prisms and cylinders, capacity in millilitres and litres, and finding an unknown dimension.
Volume
$A$ is the area of the cross-section (the end shape) and $h$ is the length or height of the solid.
A cylindrical tank has radius $10$ cm and height $20$ cm. How many litres does it hold?
A cylinder has volume $100\pi$ cm³ and radius $5$ cm. Find its height.
Cylinder: radius $10$ cm, height $20$ cm. Capacity in litres (2 d.p.)?
$2000\pi$ cm³.
Cylinder volume $100\pi$, radius $5$. Height?
$25\pi h = 100\pi$.
Volume of a $5 \times 3 \times 2$ prism?
$5 \times 3 \times 2$.
Triangular prism: end is a $3, 4, 5$ right triangle, length $10$. Volume?
$6 \times 10$.
Cylinder: radius $3$, height $10$. Volume (2 d.p.)?
$90\pi$.
How many litres in $2$ m³?
$1$ m³ $= 1000$ L.
Doubling both the radius and the height of a cylinder multiplies its volume by?
$\pi(2r)^2(2h) = 8\pi r^2h$.
A prism has cross-section area $24$ cm² and length $5$ cm. Volume?
$24 \times 5$.
New numbers every time. Keep going until you get five in a row.