Geom_Week 17_Activity 2: Missing Dimensions

Front

What is the formula for the volume of a sphere?

Back

The volume V of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

If the ratio of the lengths of the radii of two spheres is 3:5, what is the ratio of their volumes?

Back

The ratio of the volumes of the two spheres is 27:125.

Front

What happens to the volume of a cylinder if the radius is doubled while keeping the height constant?

Back

If the radius is doubled, the volume of the cylinder increases by a factor of 4, since volume V = πr²h.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

How do you find the ratio of the volumes of two spheres given their radii?

Back

The ratio of the volumes of two spheres is the cube of the ratio of their radii.

Front

What is the relationship between the volume of a sphere and its radius?

Back

The volume of a sphere increases with the cube of its radius.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

If the volumes of two spheres are in a ratio of 1:8, what is the ratio of their radii?

Back

The ratio of their radii is 1:2.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the formula for the volume of a cylinder?

Back

The volume V of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

If a cylindrical container's volume is quadrupled while keeping the height the same, how does the radius change?

Back

The radius of the new container will be 2 times larger than the original.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the significance of the ratio in geometry?

Back

Ratios in geometry help compare sizes and relationships between different geometric figures.

Tags

CCSS.1.G.A.1

CCSS.2.G.A.1

Front

How do you calculate the volume of a sphere with a radius of 3 cm?

Back

Using the formula V = (4/3)π(3)³, the volume is 36π cm³.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3