![]() There is a green tick next to the triangular and pentagonal prisms. The fourth image is a cylinder and has a circle for its cross section. The third image is a pentagonal prism and has a pentagon for its cross section. The second image has an equilateral triangle for its cross section. The first image has a right angled triangle for its cross section. The first and second images are triangular prisms. Each image shows a three dimensional shape. Previous image Next image Slide 1 of 9, A series of four images. Multiply the perimeter of the end face by the length of the prism.Work out the area of each rectangle separately, length × width.Work out the area of all the rectangular faces in one of two ways:.To calculate the total surface area of a prism:.The surface area is made up of the end faces and rectangular faces that join them. The cross-section of a prism is a polygon, a shape bounded by straight lines. When the cross-section is a hexagon, the prism is called a hexagonal prism.Ī cylinder close cylinder A 3D shape with a constant circular cross-section.When the cross-section is a triangle, the prism is called a triangular prism.cross-section close cross-section The face that results from slicing through a solid shape. can be named by the shape of its polygon close polygon A closed 2D shape bounded by straight lines. Volume is measured in cubed units, such as cm³ and mm³.Ī prism close prism A 3D shape with a constant polygon cross-section. of a prism is the area of its cross-section multiplied by the length. The volume close volume The amount of space a 3D shape takes up. Surface area is measured in square units, such as cm² and mm². ![]() shapes and the area of different shapes helps when working out the surface area of a prism. Measured in square units, such as cm² and m². of 3D close surface area (of a 3D shape) The total area of all the faces of a 3D shape. Understanding nets close net A group of joined 2D shapes which fold to form a 3D shape. The number of rectangular faces is the same as the number of edges close Edge The line formed by joining two vertices of a shape. at either end of the prism and a set of rectangles between them. faces close face One of the flat surfaces of a solid shape. is made up of congruent close congruent Shapes that are the same shape and size, they are identical. The surface area close surface area (of a 3D shape) The total area of all the faces of a 3D shape. The cross-section is a polygon close polygon A closed 2D shape bounded by straight lines. has a constant cross-section close cross-section The face that results from slicing through a solid shape. And since 2112 divided by eight is 264, then the volume of our smaller prism is 264 cubic inches.A prism close prism A 3D shape with a constant polygon cross-section. So the volume of our smaller prism will be 2112 times one-eighth. Since this is equivalent to a half times a half times a half, then our volume scale factor will be one-eighth. So our volume scale factor will be calculated by one-half to the third power. ![]() So since we want to find the volume of the smaller prism given the larger prism, then we can use the linear scale factor going in that direction. So we don’t need to worry about the area. In this case, we’re looking at the volume. ![]() But it will be calculated by the linear scale factor cubed.Īs an aside, if we had been looking at the area of two different two-dimensional shapes in a similar proportion, then the area scale factor would be found by squaring the linear scale factor. However, the scale factor of a volume is not the same as the linear scale factor. And it might be tempting to take our given volume for the larger prism and half it. In the question, we’re asked to find the volume of the smaller prism. To go from the bigger prism to the smaller prism, we would multiply our lengths by a half. We could say that the linear scale factor here would be to multiply by two. Therefore, to go from the smaller prism to the larger prism, we would double the lengths. We can see that the height in the smaller prism is 16 inches and the height in the larger prism is 32 inches. This means that every length in the larger prism is in the same proportion to equivalent lengths in the smaller prism. Since we’re told that these 3D shapes are similar, then we know that these will be the same shape but different sizes. Given that the triangular prisms shown are similar and that the volume of the bigger prism is 2112 cubic inches, determine the volume of the smaller prism.
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