Question

The sum of length, breadth, and height of a room is $19$ m. The length of the diagonal is $11$ m. The cost of painting the total surface area of the room at the rate of Rs. $10$ per $m^2$ is:

• A. Rs. $240$
• B. Rs. $2400$
• C. Rs. $430$
• D. Rs. $4200$

Answer 1

The correct option is B Rs. $2400$

$l+b+h=19m$ & $D=11m$

Now, $D=\sqrt{l^2+b^2+h^2}=11m$ ......(1)

$(l+b+h)=19m$

$\Rightarrow$${(l+b+h)}^2=361$

$\Rightarrow l^2+b^2+h^2+2(lb+bh+hl)=361$ ...(2)

$\Rightarrow \sqrt{l^2+b^2+h^2}=11,$ ...From (1)

Squaring on both sides,

$l^2+b^2+h^2=121$ ...(3)

From (2) and (3), we get

$121+2(lb+bh+hl)=361$

$\Rightarrow 2(lb+bh+hl)=240m^2$

$\therefore$TSA of cuboidal room$=240m^2$

Now, cost of painting TSA of room $=(10\times 240)=$ Rs. $2400$