3-dimensional shapes have faces, edges and vertices and can be viewed from different points.
Part of MathsGeometry and measure
Three cones have the same volume as one cylinder of the same diameter and height.
Remember the volume of a cylinder is \(\pi r^2 h\).
The volume of the cone is one third of the volume of the cylinder.
The formula for the volume of a cone is:
\(\text{volume of a cone} = \frac{1}{3} \pi r^2 h\)
A cone is made from a circle and a sectorclosesectorA slice of the circle, cut off by two radii. of a circle. The sector creates the curved surface of the cone.
The curved surface area of a cone can be calculated using the formula:
\(\text{curved surface area} = \pi \times r \times l\)
\(l\) is the slanted height.
The total surface area of the circular base and the curved surface is:
\(\text{total surface area of a cone} = \pi r^2 + \pi r l\)
Calculate the volume and total surface area of the cone (to 1 decimal place).
\(\begin{array}{rcl} \text{Volume} & = & \frac{1}{3} \pi r^2 h \\ & = & \frac{1}{3} \times \pi \times 3^2 \times 4 \\ & = & 37.7~\text{cm}^3 \end{array}\)
\(\begin{array}{rcl} \text{Total surface area} & = & \pi r^2 + \pi r l \\ & = & (\pi \times 3^2) + (\pi \times 3 \times 5) \\ & = & 75.4~\text{cm}^2 \end{array}\)