Worksheet: Surface Area and Volume of Composite Solids

Distributorsolidsurface.com – Understanding the surface area and volume of composite solids is an essential skill in geometry. Composite solids are three-dimensional figures that are formed by combining two or more basic shapes, such as cubes, cylinders, cones, and spheres. In this worksheet, we will explore various composite solids and practice calculating their surface area and volume. Grab a pencil and calculator, and let’s dive into the world of composite solids!

  1. Composite Solid 1: Cylinder on Top of a Cube

Consider a composite solid consisting of a cylinder placed on top of a cube. The dimensions of the cube are as follows: length = 5 cm, width = 5 cm, and height = 5 cm. The dimensions of the cylinder are as follows: radius = 2 cm and height = 6 cm.

a) Calculate the total surface area of the composite solid. b) Determine the volume of the composite solid.

  1. Composite Solid 2: Cone Inside a Hemisphere

Imagine a composite solid formed by placing a cone inside a hemisphere. The radius of the hemisphere is 4 cm, and the height of the cone is 6 cm. The radius of the cone’s base is 3 cm.

a) Find the surface area of the composite solid. b) Calculate the volume of the composite solid.

  1. Composite Solid 3: Cube with a Pyramid on Top

Visualize a composite solid consisting of a cube with a pyramid on top. The cube has side length 6 cm, and the pyramid has a base side length of 4 cm and a height of 8 cm.

a) Determine the total surface area of the composite solid. b) Find the volume of the composite solid.

  1. Composite Solid 4: Sphere Surrounded by a Cylinder
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Consider a composite solid comprising a sphere surrounded by a cylinder. The radius of the sphere is 5 cm, and the height of the cylinder is 10 cm.

a) Calculate the total surface area of the composite solid. b) Determine the volume of the composite solid.

  1. Composite Solid 5: Cone on Top of a Hemisphere

Imagine a composite solid formed by placing a cone on top of a hemisphere. The radius of the hemisphere is 6 cm, and the height of the cone is 8 cm. The radius of the cone’s base is 4 cm.

a) Find the surface area of the composite solid. b) Calculate the volume of the composite solid.

Remember to show all your work and round your answers to the nearest hundredth, if necessary.

Once you have completed the worksheet, review your answers and check your calculations. Surface area and volume calculations for composite solids can be challenging, so take your time and double-check your work. Practice makes perfect, so keep exploring composite solids and honing your geometry skills!

Note: This worksheet is designed to provide practice in calculating the surface area and volume of composite solids. It is recommended to refer to appropriate textbooks or online resources for detailed explanations and formulas related to composite solids.

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