Three-Dimensional Shapes
Math ⇒ Geometry
Three-Dimensional Shapes starts at 6 and continues till grade 12.
QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Three-Dimensional Shapes.
How you perform is determined by your score and the time you take.
When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.
See sample questions for grade 12
A cone has a base radius of 4 cm and a height of 9 cm. Calculate its volume.
A cube has a surface area of 54 cm². What is the length of one side?
A hemisphere has a volume of 36π cm³. What is its radius?
A right circular cone has a slant height of 13 cm and a base radius of 5 cm. What is its height?
A right circular cylinder has a height of 10 cm and a base radius of 3 cm. What is its volume?
A right circular cylinder has a lateral surface area of 60π cm² and a height of 10 cm. What is the radius of its base?
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?
A sphere has a surface area of 100π cm². What is its radius?
A sphere is inscribed in a cube of side 6 cm. What is the volume of the sphere?
A triangular prism has a base area of 20 cm² and a height of 10 cm. What is its volume?
If the base area of a pyramid is 25 cm² and its height is 6 cm, what is its volume?
If the volume of a sphere is 288π cm³, what is its diameter?
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 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?
A right circular cylinder has a fixed surface area S. What is the ratio of height to base radius (h/r) for which the volume is maximized?
A solid is formed by joining a hemisphere of radius r to the top of a right circular cylinder of the same radius and height h. Derive an expression for the total surface area of the solid (excluding the base of the cylinder).
A sphere is tangent to all six faces of a rectangular box with dimensions a, b, and c. What is the radius of the sphere?
