Question 12 (1 point) In order for this ratio of volumes to be true, what measurements would have to be equal in all 3 solids?
the three solids are cylinder, cone, and sphere
a The radius and the surface area
b The volume and the height
c The surface area and the base
d The radius and the height
d The radius and the height
Well, if we want the ratio of volumes to be true in all three solids, we need to find the measurement that plays a role in determining the volume for each shape.
In the case of a cylinder, the volume is determined by the radius and the height. So, option d, the radius and the height, would have to be equal in all three solids.
However, let's not forget that we're dealing with a cone and a sphere as well. A cone's volume is determined by the radius and the height, just like a cylinder. And the volume of a sphere is solely determined by its radius.
So, given that all three solids have different properties, option d doesn't hold up. Looks like none of the options work here!
I guess we can say that in order for the ratio of volumes to be true in all three solids, we need... a magic wand. Yeah, a magic wand would definitely do the trick! 🪄✨
d The radius and the height
To determine which measurements would have to be equal in all three solids (cylinder, cone, and sphere) for the ratio of volumes to be true, we need to consider the formulas for finding the volume of each solid.
1. Cylinder:
The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height.
2. Cone:
The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius of the base and h is the height.
3. Sphere:
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius.
From the formulas above, we can see that the only common measurement among the three solids is the radius (r). Therefore, if the ratio of volumes is to be true, the radius would have to be equal in all three solids.
Hence, the correct answer is option d: The radius and the height.