In the given figure,circle $P$ has a diameter of $2 \ m$ and circle $Q$ has a diameter of $1 \ m$. Find the area of the shaded region.

Find the number of bricks,each measuring $25\, cm \times 12.5\, cm \times 7.5\, cm$,required to construct a wall $12\, m$ long,$5\, m$ high,and $0.25\, m$ thick,if the sand and cement mixture occupies $5\%$ of the total volume of the wall.

The perimeter of a right-angled triangle is $90\, cm$ and its hypotenuse is $39\, cm$. Find its other sides.

If an equilateral triangle of area $X$ and a square of area $Y$ have the same perimeter,then $X$ is

The perimeter of a triangle is $30 \text{ cm}$ and its area is $30 \text{ cm}^2$. If the largest side measures $13 \text{ cm}$,then what is the length of the smallest side of the triangle? (in $\text{cm}$)

$A$ cylindrical vessel of height $5\, cm$ and radius $4\, cm$ is completely filled with sand. When this sand is poured out,it forms a right circular cone of radius $6\, cm$. What will be the height of this cone? (in $cm$)