A cuboid has a volume of 135 cm³. the area if the base of the cuboid is 15 cm². Find the height of the cuboid.
Answers
Answer:
Solution: Let length (ℓ) = 6x cm, breadth (b) = 4x cm and height (h) = 5x cm,
∴ Total surface area
= 2(ℓ × b + b × h × h × ℓ)
= 2(6x × 4x + 4x × 5x + 5x × 6x)cm2
= 2(24x2 + 20x2 + 30x2) cm2
=148x2 cm2
Given : Total surface = 2368 cm2
⇒ 148x2 = 2368
⇒ x2 = \frac{{2368}}{{148}} = 16
and x = \sqrt {16} = 4
∴ length = 6x cm = 6 × 4 cm = 24 cm,
breadth = 4x cm = 4 × 4 cm = 16 cm and
height = 5x cm = 5 × 4 cm = 20 cm
A cuboid is a three-dimensional shape with six rectangular faces. To find the height of the cuboid, we need to use its volume and the area of its base. If the volume of the cuboid is V and the area of its base is B, we can use the formula:
V = B * h
where h is the height of the cuboid. We are given that the volume is 135 cm³ and the area of the base is 15 cm², so we can substitute these values into the formula:
135 = 15 * h
To find the height, we need to divide both sides of the equation by 15:
h = 135 / 15
h = 9
Therefore, the height of the cuboid is 9 cm.
h = 9cm