16/9
Not enough information has been given but the volume of a cone is 1/3*pi*radius squared *height and its base area is pi*radius squared
729/8
No. To be similar ALL lengths must be in the same ratio. If two cylinders have the same radii, but different heights then the radii have one ratio (1:1) but the heights have a different ratio; thus they are not similar.
If the ratio of the radii is 1:3 then the ratio of volumes is 1:27.
volume goes a radius cubed so (8/5) cubed = 4.096
729:1
343:1
343:1
6 to 1
6^3=216 The volume of a cone is 1/3*pi*r^2*h. If r and h are each 6 times larger (as they are in this problem), then the volume is 6*6*6 times larger.
If the ratio is 2 : 7 then the volumes are in the ratio 8 : 343.
It is 8 : 343.
It is 27 : 343.
ratio of volumes is the cube of the ratio of lengths radii (lengths) in ratio 3 : 4 → volume in ratio 3³ : 4³ = 27 : 64
7:3
Not enough information has been given but the volume of a cone is 1/3*pi*radius squared *height and its base area is pi*radius squared
To find the ratios of the volumes of two similar cones with radii 2:3, we need to consider that volume is directly proportional to the cube of the radius. Let's assume that one cone has a radius of 2 units and another cone has a radius of 3 units. The formula for the volume of a cone is V = (1/3) * π * r^2 * h, where V represents volume, π is Pi (approximately 3.14), r stands for radius, and h indicates height. Since both cones are assumed to be similar, we can keep their heights constant. For simplicity, let's say their height is equal to 'h' units. Now we can calculate the ratio between their volumes: Volume_1 / Volume_2 = [(1/3) * π * r_1^2 * h] / [(1/3) * π * r_2^2 * h] The factors involving height cancel out due to similarity and division by itself results in 1: Volume_1 / Volume_2 = [r_1^2] / [r_2^2] Plugging in our given radii values: Volume_1 / Volume_2 = [4] / [9] Thus, the ratio between their volumes would be 4:9 or simply expressed as 4/9. Therefore, if one cone has a volume represented by x cubic units, then other similar cone will have a volume equal to (4x)/9 cubic units.