Volume and Surface Area of Pyramids, Cones, Spheres

The formula for the volume of a pyramid is $V=\frac{1}{3}B\times h$, where $B$ is the area of the base and $h$ is the height of the pyramid.

The volume of a pyramid is $V=\frac{1}{3}B\times h$. Substituting the values, $V=\frac{1}{3}\times 30\times 10=100{\text{cm}}^3$.

To calculate the surface area of the square pyramid, add the area of the base to the area of the four triangular faces: $16+4\times 10=56{\text{cm}}^2$.

The formula for the surface area of a sphere is $A=4\pi r^2$. Substituting the radius, $A=4\pi (6{)}^2=144\pi {\text{cm}}^2$.

The formula for the volume of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substituting the values, $V=\frac{1}{3}\pi (3{)}^2(5)=15\pi {\text{cm}}^3$.

The formula for the surface area of a cone is $A=\pi r^2+\pi rs$. Substituting the values, $A=\pi (4{)}^2+\pi (4)(8)=16\pi +32\pi =48\pi {\text{cm}}^2$.