Question

formula for mensuration

Answer 1

In the following formulae, l = length, b = breadth and h = height


Total surface area of cuboid = 2 (lb + bh + lh)

Length of diagonal of cuboid= √(l2+b2+h2)

Volume of cuboid = l × b × h

Answer 2

Solid cylinder

Curved (lateral) surface area=2πrh.

Total surface area=2πr(h+r).

Volume= πr^2h.

Hollow Cylinder

External curved surface area=2πRh.

Internal curved surface area= 2πrh.

Total surface area= 2π(Rh+rh+R^2-r^2).

Volume of material=π(R^2-r^2)h

Cone

Slant height=l=✓r^2+h^2

Curved surface area=πrl.

Total surface area= πr(l+r)

Volume= 1/3*πr^2h.

Solid sphere

Surface area=4πr^2

Volume=4/3*πr^3

Spherical shell

Thickness=R-r

Volume of material=4/3*(R^3-r^3)

Solid Hemisphere

Curved surface area=2πr^2

Total surface area=3πr^2

Volume=2/3*πr^3

Hemispherical Shell

Thickness of the shell=R-r

External curved surface area=2πR^2

Internal curved surface area=2πr^2

Total surface area=π(3R^2+r^2)

Volume of material=2/3π(R^3-r^3)