Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Relationships in Space: Geometry and Trigonometry in 2D and 3D, Exercise 26: Chapter review

A square-based pyramid, with the coordinates of $A(1,0,3), B(1,5,3)$ and $E(7,\sqrt{15},10)$ is shown. Find the length $AE$. [Enter the value excluding units]

Find the area of the triangle:   [Enter the value excluding units]

Find the surface area of a tetrahedron with all faces equilateral triangles of side $6 \mathrm{cm}$.

From the top of a vertical cliff $70 \mathrm{m}$ high, an observer notices a yacht at sea. The angle of depression to the yacht is $45°$. The yacht sails directly away from the cliff, and after five minutes the angle of depression is $10°$. How fast does the yacht sail in ${\mathrm{kmh}}^{-1}$?

Find the smallest angle of a triangle with side lengths $6, 7$ and $8 \mathrm{cm}$.

Find the area of the triangle with side lengths $6, 7$ and $8 \mathrm{cm}$.

The figure shows a container in the shape of a circular cylinder topped by a hemisphere. The radii of both cylinder and hemisphere is $3$ centimetres and the height of the cylinder is $7$ centimetres.

Calculate the volume of the container.  [Use $\mathrm{\pi }=3.14$]   [Enter the value excluding units]

The figure shows a container in the shape of a circular cylinder topped by a hemisphere. The radii of both cylinder and hemisphere is $3$ centimetres and the height of the cylinder is $7$ centimetres.

Calculate the total surface area of the container.  [Use $\mathrm{\pi }=3.14$]  [Enter the value excluding units]