Volume and Surface Area

The volume of a cube is given by V = a³, where a is the length of one side. In this case, a = 5 cm, so V = 5³ = 125 cm³.

The surface area of a cube is given by SA = 6a², where a is the length of one side. In this case, a = 4 cm, so SA = 6(4²) = 96 cm².

The volume of a rectangular prism is given by V = lwh, where l is the length, w is the width, and h is the height. In this case, l = 6 cm, w = 4 cm, and h = 3 cm, so V = 6 * 4 * 3 = 72 cm³.

The surface area of a rectangular prism is given by SA = 2(lw + wh + lh), where l is the length, w is the width, and h is the height. In this case, l = 5 cm, w = 3 cm, and h = 2 cm, so SA = 2((5 * 3) + (3 * 2) + (5 * 2)) = 52 cm².

The volume of a cylinder is given by V = πr²h, where r is the radius and h is the height. In this case, r = 4 cm and h = 8 cm, so V = π(4²)(8) = 300π cm³.

The surface area of a cylinder is given by SA = 2πr(r + h), where r is the radius and h is the height. In this case, r = 5 cm and h = 10 cm, so SA = 2π(5)(5 + 10) = 314 cm².

The volume of a cone is given by V = ½πr²h, where r is the radius and h is the height. In this case, r = 3 cm and h = 4 cm, so V = ½π(3²)(4) = 12π cm³.

The surface area of a cone is given by SA = πr(r + l), where r is the radius, l is the slant height, and h is the height. In this case, r = 6 cm and h = 8 cm. To find l, we use the Pythagorean theorem: l² = r² + h². Substituting the values, we get l² = 6² + 8² = 100. Therefore, l = 10 cm. Now we can calculate the surface area: SA = π(6)(6 + 10) = 150.79 cm².

The volume of a sphere is given by V = ½πr³, where r is the radius. In this case, r = 5 cm, so V = ½π(5³) = 523.6 cm³.

The surface area of a sphere is given by SA = 4πr², where r is the radius. In this case, r = 4 cm, so SA = 4π(4²) = 251.2 cm².

The volume of a rectangular prism is given by V = lwh, where l is the length, w is the width, and h is the height. In this case, l = 10 cm, w = 5 cm, and h = 3 cm, so V = 10 * 5 * 3 = 150 cm³.

The volume of a cylinder is given by V = πr²h, where r is the radius and h is the height. In this case, r = 6 cm and h = 8 cm, so V = π(6²)(8) = 288π cm³.

The volume of a cone is given by V = ½πr²h, where r is the radius and h is the height. In this case, r = 5 cm and h = 12 cm, so V = ½π(5²)(12) = 314 cm³.

The volume of a sphere is given by V = ½πr³, where r is the radius. In this case, r = 4 cm, so V = ½π(4³) = 268.08 cm³.

The surface area of a cube is given by SA = 6a², where a is the length of one side. In this case, a = 7 cm, so SA = 6(7²) = 343 cm².