Question 61

The total surface area of a hollow cuboid is 340 cm$$^2$$. If the length and the breadth of the cuboid are 10 cm and 8 cm respectively, then whatis the length of the longest stick that can be fitted inside the cuboid?

Solution

vol of cuboid = $$2\times(l\times b + b\times h +h\times l)$$

340 = $$2\times(10\times 8 + 8\times h +h\times 10)$$

h = 5$$cm$$

length of longest rod = diagonal of cuboid

diagonal of cuboid = $$\sqrt{l^2 + b^2 + h^2}$$ cm

= $$\sqrt{10^2 + 8^2 + 5^2}$$ cm

=$$3\sqrt{21}$$ cm

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