The length and breadth of a rectangular piece of land are in the ratio $5:3$. The owner spent ₹ $6000$ for fencing it from all sides at the rate of ₹ $7.50$ per metre. The difference between its length and breadth is (in metres):

$A$ cylindrical container whose diameter is $12\,cm$ and height is $15\,cm$,is filled with ice cream. The whole ice cream is distributed to $10$ children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base,find the diameter of the ice-cream cone? (in $cm$)

The smallest side of a right-angled triangle is $8\, cm$ less than the side of a square of perimeter $56\, cm$. The second largest side of the right-angled triangle is $4\, cm$ less than the length of the rectangle of area $96\, cm^2$ and breadth $8\, cm$. What is the largest side of the right-angled triangle? (in $cm$)

If the perimeter of an equilateral triangle is $12\, m$,then find its area.

An equilateral triangle is cut up into smaller equilateral triangles with side $1/6$ of the original. Find the number of triangles thus formed?

The sum of the areas of the $10$ squares,the lengths of whose sides are $20 \, cm, 21 \, cm, \ldots, 29 \, cm$ respectively is ...... $cm^2$.