Understanding 3D Shapes: Volume and Surface Area

What is the formula to calculate the volume of a prism?

• Volume = 2(Base Area) + Perimeter(Base) x Height

• Volume = (4/3)πr^3

• Volume = (1/3) Base Area x Height

• Volume = Base Area x Height

How do you calculate the surface area of a prism?

• Surface Area = Base Area x Height

• Surface Area = 2(Base Area) + Perimeter(Base) x Height

• Surface Area = (1/3) Base Area x Height

• Surface Area = 4πr^2

What is the volume formula for a triangular prism?

• Volume = (1/2) Base x Height of Triangle x Height of Prism

• Volume = 2(Base Area) + Perimeter(Base) x Height

• Volume = Base Area x Height

• Volume = πr^2 x Height

How is the surface area of a cylinder calculated?

• Surface Area = 2πr^2 + 2πrh

• Surface Area = πr^2 x Height

• Surface Area = 2(Base Area) + Perimeter(Base) x Height

• Surface Area = (1/3) Base Area x Height

What distinguishes the volume formula of pyramids and cones from prisms and cylinders?

• It uses the perimeter of the base.

• It includes the slant height.

• It is multiplied by 1/3.

• It is the same as for prisms and cylinders.

How do you find the surface area of a cone?

• Surface Area = 4πr^2

• Surface Area = 2πr^2 + 2πrh

• Surface Area = Base Area + 1/2 Perimeter(Base) x Slant Height

• Surface Area = πr(l + r)

What is the significance of the '1/3' in the volume formula for pyramids and cones?

• It represents the fraction of the volume compared to a prism or cylinder with the same base and height.

• It indicates the pyramid or cone has one-third the height of equivalent prisms or cylinders.

• It signifies that the base area must be divided by three.

• It is used to calculate the slant height of the pyramid or cone.

What is the formula for the volume of a sphere?

• Volume = 2πr^2 + 2πrh

• Volume = Base Area x Height

• Volume = πr^2 x Height

• Volume = (4/3)πr^3

How is the surface area of a sphere calculated?

• Surface Area = 4πr^2

• Surface Area = 2πr^2 + 2πrh

• Surface Area = πr(l + r)

• Surface Area = Base Area + 1/2 Perimeter(Base) x Slant Height

Why is the surface area formula for cylinders and prisms different from that of spheres?

• Because cylinders and prisms have straight edges while spheres do not.

• Because spheres do not have a base or height.

• Because spheres are not three-dimensional.

• Because the surface area of a sphere is calculated using its radius only.