Grade 9 Math: Frustums Worksheet
Explore the properties and calculations related to frustums, including surface area and volume, with this Grade 9 math worksheet.
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Grade 9 Math: Frustums
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
A frustum is a portion of a solid (usually a cone or pyramid) that remains after cutting off the top by a plane parallel to the base. It has two parallel bases and a lateral surface.
1. Which of the following is NOT a characteristic of a frustum?
Two parallel bases
Lateral faces are always triangles
Formed by cutting off the top of a cone or pyramid
Can be a frustum of a cone or a pyramid
2. The formula for the volume of a frustum of a cone is V = (1/3)πh(R² + Rr + r²). What does 'r' represent?
Radius of the larger base
Radius of the smaller base
Slant height
Height of the frustum
1. A frustum is formed by cutting off the top of a or a by a plane parallel to the base.
2. The lateral surface of a frustum of a cone is a part of a .
3. The volume of a frustum of a pyramid is given by V = (1/3)h(A₁ + A₂ + √A₁A₂), where A₁ and A₂ are the areas of the bases.
1. A frustum of a cone has a height of 8 cm, and the radii of its two circular bases are 10 cm and 4 cm. Calculate the volume of the frustum. (Use π ≈ 3.14)
2. Explain the difference between a frustum of a cone and a complete cone.
Consider a frustum of a square pyramid with the following dimensions:
Side length of the larger square base (s₁): 10 cm
Side length of the smaller square base (s₂): 4 cm
Height of the frustum (h): 6 cm
Calculate the volume of this frustum of a square pyramid.
1. The lateral surface area of a frustum of a cone is always a rectangle.
True
False
2. A frustum of a pyramid has two bases that are similar polygons.
True
False