Surface Area of Solids

Rarely Tested




TYPE OF SOLIDLATERAL S.A.TOTAL S.A.
Cube (all sides equal to a)4a26a2
Cuboid (length l, breadth b, height h)2(l + b)h2(lb + bh + hl)
Right Circular Cylinder (radius r, height h)2πrh2πr(h + r)
Right Circular Cone (radius r, height h, slant height l)πrlπr(l + r)
Cone frustum (radii $$r_1$$, $$r_2$$, height h and slant height l)$$\pi(r_1+r_2)l$$$$\pi[(r_1+r_2)l+(r_1^2+r_2^2)]$$
Sphere (radius r)4πr24πr2
Solid Hemisphere (radius r)2πr23πr2
Pyramid$$\frac{1}{2}\times\ Perimeter\times\ Slant\ Height$$$$Curved\ Surface\ area+Base\ area$$
Prism$$Perimeter\times\ Height$$$$Curved\ Surface\ area+2\times\ Base\ area$$




Slant height of cone: l = $$\sqrt{(r² + h²)}$$
Slant height of frustum: l = $$\sqrt{(h² + (r₁−r₂)²)}$$
Diagonal of cuboid: $$\sqrt{(l² + b² + h²)}$$
Diagonal of cube: a$$\sqrt3$$
Euler's formula for 3D figures (specifically closed) states that the number of faces (F) plus the number of vertices (V) minus the number of edges (E) always equals 2: $$F+V-E\ =\ 2$$.

Formula Video


Question 1

A cube is dropped into water and is then cut into 64 small cubes. How many of these smaller cubes are wet on exactly two of their sides?

Question 2

Suppose the volume of a football is 700% more than the volume of a cricket ball. By how much percent is the surface area of the football greater than the cricket ball?

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