Volume of a Cube
Total space occupied by a cube is called the volume of
that cube. A cube is a solid object having six square faces of equal size, therefore its
length, breadth and height all are equal. Volume of a cube is given by the
product of its length, length and length i.e length cube.
∴ Volume of a Cube (V) = l × l × l = l3
********************
10 Math Problems officially announces the release of Quick Math Solver and 10 Math Problems, Apps on Google Play Store for students around the world.
********************
********************
Workout Examples
Example 1: Find the volume of the given solid figure.
Solution: The given solid
figure is a cube of length (l) 8cm,
∴ Volume of cube = l3
= (8cm)3
= 8cm × 8cm × 8cm
= 512 cm3
Example 2: If the total surface area of a cubical box is 486cm3,
find its volume.
Solution: Here,
T.S.A. of cubical box
= 486cm2
i.e. 6l2 = 486
or, l2 = 486/6
or, l2 = 81
or, l = 9cm
∴ Volume of cubical box = l3
=
(9cm)3
=
9cm × 9cm × 9cm
=
729cm3
Example 3: If the volume of cubical block is 1728cm3,
Find:
a. Total surface area of the block.
b. The cost of painting its surface at Rs. 10 per square cm.
Solution: Here,
Volume of cubical block = 1728c
i.e. l3 = 1728
or, l = 12cm
a. ∴ Total surface area of the
block = 6l2
= 6 × (12cm)2
= 6 × 144cm2
= 864cm2
b. Rate of painting = Rs. 2
per cm2
∴ Cost of painting =
Rate × Area
= Rs. 10 × 864
= Rs. 8640
You can comment your questions or problems
regarding the area and volume of cube here.
0 comments: