A frustum of a cone has a top radius of 3 cm, a bottom radius of 5 cm, and a height of 7 cm. What is the volume of the frustum?

Fri, 17 Apr 2026 05:56:10 +0000

**How Does the Volume of a Frustum of a Cone Calculate? A Curious Deep Dive for US Learners** Ever wondered how engineers determine the space inside a shaped object that’s neither a full cylinder nor a solid cone? One such fascinating structure is the frustum of a cone—where the base and top surfaces are circular, with the top smaller than the bottom, and a steady slope between them. This geometric shape appears more often than you might expect, from architectural details in modern buildings to packaging design and industrial manufacturing. Understanding its volume isn’t just a math exercise—it reveals the practical intelligence behind everyday objects and design. When someone asks, “What is the volume of a frustum of a cone with a top radius of 3 cm, bottom radius of 5 cm, and height of 7 cm?” they’re tapping into a real-world question about space, proportion, and structural efficiency. Though the term “frustum” sounds technical, the calculation follows clear, linear principles rooted in geometry—ideal for mobile learners seeking clarity without jargon. ### The Formula in Context
The volume of a frustum of a cone is determined by subtracting the smaller cone (a known shape) from the larger cone. With radii of 5 cm and 3 cm and a height of 7 cm, the volume depends on a simple formula involving radius, height, and the difference in squared radii. This balance ensures accurate spatial calculations critical in construction, manufacturing, and product design.