Please enter the following details
Free Daily Targets & Mocks
Study Material & Formulas PDFs
1 on 1 Mentorship
Question 79
Surface area of a cuboid is 22 $$cm^2$$ and the sum of the lengths of all its edges is 24 cm. The length of each diagonal of the cuboid, in cm, is
Solution
Let length, breadth and height be $$l,b,h$$ cm respectively.
=> Surface area of cuboid = $$(lb+bh+hl)=281$$ -----------(i)
Sum of all edges = $$(l+b+h)=24$$
Squaring both sides, => $$(l^2+b^2+h^2)+2(lb+bh+hl)=576$$
Substituting value from equation (i), we get :
=> $$(l^2+b^2+h^2)+2(281)=576$$
=> $$(l^2+b^2+h^2)=576-562=14$$
$$\therefore$$ Diagonal of cuboid = $$\sqrt{l^2+b^2+h^2}=\sqrt{14}$$
=> Ans - (D)
