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 rectangular box has dimensions 3 cm × 4 cm × 5 cm. What is its space diagonal length?

A regular hexagonal prism has a base edge of 2 cm and a height of 8 cm. What is its volume? (Area of regular hexagon = (3√3/2)a²)

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 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?