A cube whose edge is $21 cm$ long has a circle of diameter $21 cm$ each of its faces painted black. What is the total area of the unpainted surface of the cube?

Three solid metal cubes of sides $6 cm, 8 cm \text{and} 10 cm$ are melted and formed into a new cube. Find the side of the new cube.

The figure alongside represents the horizontal cross-section of a pond. $ABDE$ is an isosceles trapezium in which $AE = 1 m, ED = 5 m, BD = 7 m$. $BCD$ is a semicircle on diameter $BD$. The sides of the pond are vertical and the depth of the water in the pond is $50 cm$. Find the perimeter of the given cross-section.

The figure alongside represents the horizontal cross-section of a pond. $ABDE$ is an isosceles trapezium in which $AE = 1 m, ED = 5 m, BD = 7 m$. $BCD$ is a semicircle on diameter $BD$. The sides of the pond are vertical and the depth of the water in the pond is $50 cm$. Find the area of the sides in contact with water.

A closed storage container consists of a cuboid$ABDEPOST$  to which a quadrant of a cylinder $BCDQRS$ is attached as shown in the figure. $AE= 20 cm, ED = 30 m, DC= 20 cm$ and $CR=70 cm$. Taking $\mathrm{\pi }=3.14$

Calculate the length of the arc $BCD$

The diagram represents the floor of a room. All dimensions are in metres and all the angles are right angles. Calculate the perimeter of the room

A closed rectangular box is made of wood of $1.5 \mathrm{cm}$ thickness. The external length and breadth are $78 \mathrm{cm}$ and $19 \mathrm{cm}$ and the capacity of the box is $15000 {\mathrm{cm}}^3$. The external height of the box is $a cm$. Find the value of $a.$