ABC26GN4818 · Volume and Surface Area
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is $5 \sqrt{5} \mathrm{cm}$. It surface area is
(a)$125 \mathrm{cm}^{2}$
(b)$236 \mathrm{cm}^{2}$
(c)$361 \mathrm{cm}^{2}$
(d)$486 \mathrm{cm}^{2}$
Answer
Explanation
$(l+b+h)=19$ and $$\sqrt{l^{2}+b^{2}+h^{2}}=5 \sqrt{5} \text { and so }\left(l^{2}+b^{2}+h^{2}\right)=125 .$$ Now, $(l+b+h)^{2}=19^{2} \Rightarrow\left(l^{2}+b^{2}+h^{2}\right)+$ $$2(l b+b h+l h)=361$$ $\Rightarrow 2(l b+b h+l h)=(361-125)=236$. ∴ Surface area $=236 \mathrm{cm}^{2}$.
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