Real-Life Math
A woman drives up in a vintage Morris Minor and parks in front of
your stereo shop. You go outside and she shows you an old radio installed
in her car. She wants to take out the old radio and replace it with a new
stereo.
She has the new stereo at home, which measures 23 cm long x
12 cm wide x 10 cm high. "Will the new stereo fit in the same spot as the
old radio, without having to cut a new hole in the dash?" she asks.
"You
have to calculate box sizes and constantly figure out volumes and square areas
of different systems to see if they will fit or not," says Sandy MacDonald,
a car stereo installer.
You ask your assistant to measure the old radio
in the car. If it is the same size or larger than the new stereo, then you
won't have to cut a hole in the dash to install the new stereo.
In
a few minutes, your assistant returns with the measurements of the radio.
It measures 10 inches long x 6 inches wide. The volume of the radio is 240
cubic inches.
Inches? You wanted the measurements in centimeters! And
how are you supposed to know if the new stereo will fit if you don't know
the height of the old radio?
You rush out to the street,
but the woman is gone. You will have to use the information your assistant
gave you.
Will the new stereo fit in the old radio's spot, or will
you have to enlarge the hole in the dash?
Hint: Use the volume of the
radio to calculate its height. Then convert the dimensions of the radio into
centimeters, so that you can compare them with the dimensions of the new stereo.