Question

solve it anyone. please solve step by step give me. immediately needed.

Answer 1

Let the length, breadth and depth of the cylinder be a, b and c


Given, a + b + c = 19 cm

Diagonal = 5√5 cm.


Diagonal of a cylinder is given as :-

$\sqrt{ {a}^{2} + {b}^{2} + {c}^{2} }$


So diagonal =
$\sqrt{ {a}^{2} + {b}^{2} + {c}^{2} } = 5 \sqrt{5}$
Square both the sides

=>
${a}^{2} + {b}^{2} + {c}^{2} = (5 \sqrt{5} ) {}^{2}$


Now, a² + b² + c² is also written as
= (a + b + c)² - 2(ab + bc + ca)

=>
$(a + b + c) {}^{2} - 2(ab + bc + ca) = ( 5\sqrt{5} ) {}^{2}$


Now given a + b + c = 19

=>
${19}^{2} - 2(ab + bc + ca) = 125 \\ \\ = > 361 - 2(ab + bc + ca) = 125 \\ \\ = > - 2(ab + bc + ca) = 125 - 361 \\ \\ = > - 2(ab + bc + ca) = - 236 \\ \\ = > 2(ab + bc + ca) = 236$

Now, the surface area of cuboid is = 2(lh + bh + lb)

here, l = a, b = b, h = c

=> 2(ab + bc + ca) = surface area

and 2(ab + bc + ca) = 236

=> surface area = 236 cm²


Answer :- 236 cm²