Question
Download Solution PDFThe sum of the length, width and depth of a cuboid is 8 cm and its diagonal is 5 cm. What is its surface area?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Length + Width + Height = 8 cm
Diagonal = 5 cm
Formula used:
Diagonal2 = l2 + w2 + h2
Surface Area = 2 × (lw + wh + hl)
Calculation:
Let l + w + h = 8 ...(i)
⇒ Diagonal2 = 52 = 25
⇒ l2 + w2 + h2 = 25 ...(ii)
Now, (l + w + h)2 = l2 + w2 + h2 + 2(lw + wh + hl)
⇒ 82 = 25 + 2(lw + wh + hl)
⇒ 64 = 25 + 2(lw + wh + hl)
⇒ 2(lw + wh + hl) = 39
⇒ lw + wh + hl = 19.5
Surface Area = 2 × 19.5 = 39 cm2
∴ The surface area is 39 cm².
Last updated on Jul 16, 2025
-> More than 60.65 lakh valid applications have been received for RPF Recruitment 2024 across both Sub-Inspector and Constable posts.
-> Out of these, around 15.35 lakh applications are for CEN RPF 01/2024 (SI) and nearly 45.30 lakh for CEN RPF 02/2024 (Constable).
-> The Examination was held from 2nd March to 18th March 2025. Check the RPF Exam Analysis Live Updates Here.