Three-Dimensional Shapes
Math ⇒ Geometry
Three-Dimensional Shapes starts at 6 and continues till grade 12.
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See sample questions for grade 12
A solid has 20 faces, 30 edges, and 12 vertices. What is the name of this solid?
A solid has 6 faces, all of which are rectangles. What is the name of this solid?
State Euler’s formula for convex polyhedra.
State the difference between a prism and a pyramid.
A cube has a volume of 216 cm³. If a sphere is inscribed inside the cube, what is the surface area of the sphere?
A frustum of a right circular cone has base radii r1 and r2 (r1 > r2) and height h. Write the formula for its volume.
A regular octahedron is made by joining two square-based pyramids at their bases. If the edge length is a, what is the total surface area of the octahedron?
A regular tetrahedron is inscribed in a sphere of radius R. Express the edge length a of the tetrahedron in terms of R.
A right circular cone and a right circular cylinder have the same base radius r and the same height h. What is the ratio of the volume of the cone to the volume of the cylinder?
Which of the following is a Platonic solid?
(1) Square pyramid
(2) Icosahedron
(3) Pentagonal prism
(4) Truncated cube
Which of the following is NOT a polyhedron?
(1) Cube
(2) Sphere
(3) Tetrahedron
(4) Dodecahedron
Which of the following is NOT a property of a regular octahedron?
(1) 8 faces
(2) 12 edges
(3) 6 vertices
(4) All faces are squares
Which of the following is true for all Platonic solids?
(1) All faces are congruent regular polygons
(2) All faces are rectangles
(3) All have more than 20 faces
(4) All have at least 10 vertices
Fill in the blank: The number of faces of a dodecahedron is ______.
The total surface area of a cube with side length 5 cm is ______ cm².
The volume of a regular tetrahedron with edge length a is ______.
Is it possible for a polyhedron to have 7 faces, 10 vertices, and 15 edges?
True or False: All faces of a regular tetrahedron are equilateral triangles.
True or False: The sum of the face angles at each vertex of a regular polyhedron is always less than 360°.
True or False: The surface area of a sphere is four times the area of a great circle of the sphere.
