#### Chapter 5 Geometry

Section 5.5 Simple Geometric Solids

# 5.5.3 Exercises

##### Exercise 5.5.9
Calculate the volume of a prism of height $h=8 \mathrm{cm}$ with a triangle as its base. Two sides of this triangle are of length $5 \mathrm{cm}$, and one side is of length $6 \mathrm{cm}$.
$\mathrm{cm}{}^{3}$

##### Exercise 5.5.10
The surface area of a cylinder of height $h=6 \mathrm{cm}$ is to be covered with a coloured sheet. The surface area shall be $O=200 \mathrm{cm}{}^{2}$. Calculate the diameter $d$ of the disk and the volume of the cylinder. Use the approximate value $3.1415$ for $\pi$ and round off your result to the nearest millimetre.
1. $d$$=$
$\mathrm{cm}$
2. $V$$=$
$\mathrm{cm}{}^{3}$
Consider a piece of wood with the shape of a rectangular cuboid with the volume $V$. The height of the cuboid is $h=120 \mathrm{cm}$, and the base face is a square with sides of length $s=40 \mathrm{cm}$. From the piece of wood, a cylindrical hole of height $g$ with a diameter $d=20 \mathrm{cm}$ is drilled "centrically" (i.e. the intersection point of the diagonals of the quadratic base face is the centre of the base disk of the cylinder). Use the approximate value $3.1415$ for $\pi$ and round off your result to integers. Calculate
1. the volume ${V}_{Z}$ of the drilled hole:
${V}_{Z}$$=$
$\mathrm{cm}{}^{3}$
2. the percentage of the volume ${V}_{1}$ of the new piece of wood remaining after drilling of the volume ${V}_{0}$:
$%$