##### VOLUME AND SURFACE AREA

*CUBOID*Let length =*l*, breadth =*b*and height =*h*units. Then*Volume*= (*l*x*b*x*h*) cubic units.*Surface area*= 2(*lb*+*bh*+*lh*) sq. units.*Diagonal*=*l*^{2}+*b*^{2}+*h*^{2}units.

*CUBE*Let each edge of a cube be of length*a*. Then,*Volume*=*a*^{3}cubic units.*Surface area*= 6*a*^{2}sq. units.*Diagonal*= 3*a*units.

*CYLINDER*Let radius of base =*r*and Height (or length) =*h*. Then,*Volume*= (*r*^{2}*h*) cubic units.*Curved surface area =*(2*rh*) sq. units.*Total surface area*= 2*r*(*h*+*r*) sq. units.

*CONE*Let radius of base =*r*and Height =*h*. Then,*Slant height,**l*=*h*^{2}+*r*^{2}units.*Volume*=*r*^{2}*h*cubic units.*Curved surface area*= (*rl*) sq. units.*Total surface area*= (*rl*+*r*^{2}) sq. units.

*SPHERE*Let the radius of the sphere be*r*. Then,*Volume*=*r*^{3}cubic units.*Surface area*= (4*r*^{2}) sq. units.

*HEMISPHERE*Let the radius of a hemisphere be*r*. Then,*Volume*=*r*^{3}cubic units.*Curved surface area*= (2*r*^{2}) sq. units.*Total surface area*= (3*r*^{2}) sq. units.Note: 1 litre = 1000 cm^{3}.#### A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

#### The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.

#### A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:

#### The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.

#### 15. How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?