The perimeter of an equilateral triangle is $72 \sqrt{3} \text{ cm}$. Find its height in meters.

The volume of two hemispheres is in the ratio $8:27$. What is the ratio of their radii?

In the given figure,there is a large semicircle with diameter $AB = 56 \ cm$. Inside this,there are four smaller identical semicircles with diameters $AE, EF, FG,$ and $GB$ along the diameter $AB$. $A$ circle is inscribed such that it is tangent to the large semicircle and the two middle smaller semicircles. What is the area (in $cm^2$) of the shaded region?

The area of the circumcircle of an equilateral triangle is $3 \pi \, cm^2$. The perimeter of the triangle is

The base of a triangular field is three times its height. If the cost of cultivating the field at ₹ $36.72$ per hectare is ₹ $495.72$,then find its base and height.

$A$ circle and a rectangle have the same perimeter. The sides of the rectangle are $18 \, cm$ and $26 \, cm$. What is the area of the circle? (in $cm^2$)