Page 362 - Math Smart - 7

Calculate the volume and surface area of each of these cuboids.
a)

30 mm
3.2 cm
5 cm
20 mm
3.2 cm

Peter builds a cupboard 2 m high on a square base with sides measuring 600 mm.
a) Calculate the perimeter of the square base.
b) Calculate the area of one of the vertical faces of the cupboard.
c) Calculate the volume of the cupboard in m^.
d) Calculate the surface area of the cupboard in m^.
e) Peter wants to paint the outside of the cupboard, but not its base.
Calculate the surface area that needs to be painted.
f) Peter starts painting at 09 30 and finishes painting at 13 05.
How long did it take for Peter to paint the cupboard?

Mathematics Connect

In 1583. Italian physicist Galileo Galilei discovered that
a pendulum always takes the same amount of time to
swing back and forth. So, in the past, pendulums were
used to make clocks because a pendulum provides a
regular indicator of time passed. If the string of the
pendulum is about 25 cm, it makes a 1-second swing,
back and forth. This in turn moves the gears in the clock
every 1 second, causing the hour and minute hands
in the clock to move, to show time. But a problem is
that air resistance and friction uses up the pendulum's
kinetic energy, and the clock will stop working when
the pendulum stops moving. Pendulum clocks also
due to gravity given its tiny size, it varies its swing by
depends on gravity to move. If there is a change in
pressure and temperature. So. a quartz clock may lose
gravity, like deep under the sea or high up on the
time over the years.
mountains, the clock will tell time that is either too fast
or too slow. Recently, scientists built the most accurate clock that
loses only 1 second every 15 billion years. It is made of
To solve this problem, we found quartz. Inside a quartz
strontium, which makes use of the regular vibrations
clock or watch, the battery sends electricity to the
of an atom between two energy states. Accurate clocks
quartz crystal, causing the quartz crystal to move back
play an important role in determining the accuracy
and forth exactly 32768 times each second. The circuit
of GPS satellites in navigation and global positioning
then sends out electric pulses, one per second. These
technology. The Strontium clock is so accurate, and
pulses power the watch display to show digital time or
sensitive to minute changes in gravity, that physicists
the pulses turn the gears that move the clock's hands.
are thinking of using it to map out the shape of the
Although the quartz crystal is not affected greatly
Earth!
Measuring Time, Area, Perimeter and Volume