Volume and Surface Area of Solids

The volume of a cube is given by (s^3), where (s) is the length of one side of the cube.

The surface area of a cube is given by (6s^2), where (s) is the length of one side of the cube.

The volume of a sphere is given by (\frac{4}{3}\pi r^3), where (r) is the radius of the sphere.

The surface area of a sphere is given by (4\pi r^2), where (r) is the radius of the sphere.

The volume of a cylinder is given by (\pi r^2 h), where (r) is the radius of the base and (h) is the height of the cylinder.

The surface area of a cylinder is given by (2\pi r h + 2\pi r^2), where (r) is the radius of the base and (h) is the height of the cylinder.

The volume of a cone is given by (\frac{1}{3}\pi r^2 h), where (r) is the radius of the base and (h) is the height of the cone.

The surface area of a cone is given by (\pi r h + \pi r^2), where (r) is the radius of the base and (h) is the height of the cone.

Since the volume of a cube is (s^3), where (s) is the length of one side, we can solve for (s) by taking the cube root of the volume. (\sqrt[3]{64} = 4), so the length of one side of the cube is (4) cm.

The volume of a sphere is given by (\frac{4}{3}\pi r^3). Substituting (r = 5) cm, we get (\frac{4}{3}\pi (5)^3 = 523.6) cm³.

The volume of a cylinder is given by (\pi r^2 h). Substituting (r = 3) cm and (h = 8) cm, we get (\pi (3)^2 (8) = 75.4) cm³.

The volume of a cone is given by (\frac{1}{3}\pi r^2 h). Substituting (r = 4) cm and (h = 10) cm, we get (\frac{1}{3}\pi (4)^2 (10) = 33.5) cm³.

The surface area of a cube is given by (6s^2), where (s) is the length of one side. Solving for (s), we get (s = \sqrt{\frac{A}{6}}). Substituting (A = 150) cm², we get (s = \sqrt{\frac{150}{6}} = 5) cm.

The surface area of a sphere is given by (4\pi r^2). Solving for (r), we get (r = \sqrt{\frac{A}{4\pi}}). Substituting (A = 144) cm², we get (r = \sqrt{\frac{144}{4\pi}} = 4) cm.

The surface area of a cylinder is given by (2\pi r h + 2\pi r^2). Solving for (h), we get (h = \frac{A - 2\pi r^2}{2\pi r}). Substituting (A = 300) cm², (r = 5) cm, and (\pi \approx 3.14), we get (h = \frac{300 - 2\pi (5)^2}{2\pi (5)} = 10) cm.