Final answer:
To find the base area of the box, I solved the relationships given between length, breadth, and height in terms of the height, substituted the volume into the resulting equation, and found the height to calculate the breadth. The base area turned out to be 36 cm², which corresponds to option c.
Step-by-step explanation:
The question asks us to find the area of the base of a box given that the box's length is twice its breadth and thrice its height, and it has a volume of 288 cm³. Let's denote the breadth as b, the height as h, and the length as l. Based on the given information, l = 2b and l = 3h, which implies b = 1.5h. The volume V of a box is calculated as V = l × b × h.
Using the relationships between the length, breadth, and height, we can express the volume as V = 3h × 1.5h × h = 4.5h³. We know that the volume is 288 cm³, so 4.5h³ = 288. Solving this, we get h³ = 64 and h = 4 cm. Thus the breadth b = 1.5 × 4 = 6 cm and the area of the base of the box is b × b = 6 cm × 6 cm = 36 cm².
The correct answer for the base area of the box is 36 cm², which matches option c.