MYP Standard Mathematics Topic 7.2 Volume Questionbank

Consider a cone with base radius $r$ and vertical height $h = r$ . A sphere also has radius $r$ . What is the ratio of the volume of this specific cone to the volume of the sphere?

True or False: If a sphere has a volume of $V$ , then the volume of the smallest cylinder that can circumscribe it is exactly $\frac{3}{2}V$ .

Based on the geometric relationship attributed to Archimedes, the volume of a sphere is exactly what fraction of the volume of the cylinder that just fits around it (the circumscribed cylinder)?

True or False: If a sphere has a radius $r$ , the volume of the 'tightest' cylinder that can hold it (the circumscribed cylinder) is given by the formula $V = 2\pi r^3$ .

Archimedes established that the volume of a sphere is two-thirds the volume of its circumscribed cylinder. If the cylinder that perfectly encloses a sphere has a volume of $30\pi\text{ cm}^3$ , what is the volume of the sphere?

MYP Standard Mathematics 7.2 Volume Questionbank

MYP Standard Mathematics 7.2 Volume Questionbank

MYP Standard Mathematics 7.2 Volume Questionbank

MYP Standard Mathematics 7.2 Volume Questionbank

MYP MYP Standard Mathematics Topic 7.2 Volume Questionbank