$A$ room without a ceiling is $12 \, m$ long,$4 \, m$ wide,and $3 \, m$ high. Find the length of the longest rod that can be placed in that room. (in $m$)

The length,breadth,and height of a metallic cuboid are $10\, cm$,$6\, cm$,and $4\, cm$ respectively. If the density of the metal is $7.8\, g/cm^3$,find the mass of the cuboid (in $g$).

The radii of five metal spheres are $1\, cm, 3\, cm, 4\, cm, 5\, cm$ and $8\, cm$ respectively. If they are melted and cast into a single large sphere,find the radius of that sphere. Furthermore,if this large sphere is melted and recast into smaller cylinders,each with a radius of $3\, cm$ and a height of $4\, cm$,how many such cylinders can be formed?

The surface area of a sphere is $7850 \, cm^2$. Find its radius in $cm$. (Use $\pi = 3.14$)

Metal spheres,each of radius $2 \, cm$,are packed into a rectangular box of internal dimensions $16 \, cm \times 8 \, cm \times 8 \, cm$. When $16$ spheres are packed,the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [Use $\pi = 3.14$] (in $cm^3$)

$A$ cuboidal closed tank of iron sheet is made having $10 \, m$ length,$8 \, m$ breadth,and $3 \, m$ height. Determine the cost of iron sheet used at the rate of $₹ 50$ per $m^2$. (in $₹$)