Module 4
CLASS IX
MATHS
CCT
1. JUICY WATERMELONS
Cubic watermelons are watermelons grown into the shape of a cube. This is
generally intended for space efficiency in small refrigerators. The practice of
growing cube watermelons is popular in Japan. The melons are grown in boxes
and assume the shape of the container. Normal watermelons are round in nature.
QUESTION 1.1:
If the side of a cubical watermelon is equal to the diameter of a spherical watermelon and they
are to be stacked in boxes, then which one would occupy more space than the other?
QUESTION 1.2:
If 90% of the watermelons are full of water, then how much water (juice) will you get from
the cubic watermelon of side 15cm.
Answers
Given,
The side of the cubical watermelon = The diameter of spherical watermelon.
To find,
The watermelon which has greater volume.
Solution,
We can simply solve this mathematical problem by using the following mathematical process.
Let, the side of the cubical watermelon = 4 cm [Assumed for general demonstration, and the rest of the calculation method will be applicable for any value.]
Diameter of the spherical watermelon = 4 cm
Radius of the spherical watermelon = 4/2 = 2 cm
Volume of cubical watermelon = (4)³ = 64 cm³
Volume of spherical watermelon = 4/3 × π × (2)³ = 33.51 cm³
Volume of cubical watermelon > Volume of spherical watermelon.
And again, this conclusion is applicable for any value of the length of side of cubical watermelon or radius of spherical watermelon.
Hence, the cubical watermelon will occupy more space.
____________________________________________
Given,
90% of the watermelon is full of water.
side of cubical watermelon = 15 cm
To find,
Amount of water.
Solution,
We can simply solve this mathematical problem by using the following mathematical process.
Volume of the total watermelon = (15)³ = 3375 cm³
Volume of the water = 3375 × 90/100 = 3037.5 cm³
Volume of water in litres = 3.0375 litres
Hence, we will get 3.0375 litres of water.
Step-by-step explanation:
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