A cube and cuboid have the same base area. The volume of the cube is 64cm\(^3\) while that of the cuboid is 80cm\(^3\). Find the height of the cuboid
A
1cm
B
3cm
C
5cm
D
6cm
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Volume of a cube with side a cm = a\(^3\)
a\(^3\) = 64 \(\implies\) a = 4cm
Base area of a cube = a\(^2\)
= 4\(^2\)
= 16 cm\(^2\)
\(\implies\) Base area of the cuboid = 16 cm\(^2\)
Volume of cuboid = Base area x height
80 = 16 x h
h = \(\frac{80}{16}\)
= 5 cm
Source: Myschool Past Questions Archive (Record #36870)