Volume and Surface Area of Pyramids, Cones, Spheres

Feedback: Not quite! 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.

Feedback: Not quite! The volume of a pyramid is $V = \frac{1}{3} B \times h$, where $B$ is the base area and $h$ is the height. Substituting the values, $V = \frac{1}{3} \times 30 \times 10 = 150 \, \text{cm}^3$.

Feedback: Not quite! To calculate the surface area of the square pyramid, add the area of the base to the area of the four triangular faces: $16 \, \text{cm}^2 + 4 \times 10 \, \text{cm}^2 = 56 \, \text{cm}^2$.

Feedback: Not quite! The formula for the surface area of a sphere is $A = 4\pi r^2$. Substituting the radius, $A = 4\pi (6)^2 = 144\pi \, \text{cm}^2$.

Feedback: Not quite! The formula for the volume of a cone is $V = \frac{1}{3} \pi r^2 h$. Substituting the values, $V = \frac{1}{3} \pi (3)^2 (5) = 15\pi \, \text{cm}^3$.

Feedback: Not quite! The formula for the surface area of a cone is $A = \pi r^2 + \pi r s$. This formula comes from adding the area of the base (a circle, which is $\pi r^2$) and the lateral surface area (which unfolds into a sector of a circle and has an area of $\pi r s$). Substituting the values, we get $A = \pi (4)^2 + \pi (4)(8) = 16\pi + 32\pi = 48\pi \, \text{cm}^2$.