a cylindrical block weighs 6 kg. how much will another cube of the same metal weigh if its sides are twice as long?
volume is proportional to the cube of the corresponding sides
so if sides are doubled, volume is 2^3 or multiplied by a factor of 8
so new cube would weigh 48 kg
To find out the weight of the cube, we need to compare its volume with the volume of the cylindrical block.
First, let's find the volume of the cylindrical block. The volume of a cylinder is given by the formula: V_cylinder = π * r^2 * h, where π is approximately 3.14, r is the radius, and h is the height.
Since the shape is a cylinder, we assume the sides are the same length, making it a perfect cylinder. Therefore, we can assume that the radius (r) is half the side length (s) of the cube.
Now, let's find the volume of the cylinder.
Given:
Weight of cylindrical block = 6 kg
Since the weight is not related to volume, we can ignore it for now.
We need to find the volume by calculating the radius (r) and height (h) of the cylinder. However, the problem doesn't provide any information about the dimensions of the cylinder, so it is not possible to find the exact volume of the cylinder at this point.
To find the weight of the cube, we need to compare the volume of the cube with the cylinder and consider that they are made of the same metal.
The cube has sides twice as long as the sides of the cylindrical block. Therefore, the ratio of the sides of the cube to the sides of the cylinder is 2:1. Since volume is directly proportional to the cube of the side length (V_cube = s^3), the volume of the cube will be (2^3) = 8 times greater than the volume of the cylinder.
Since the volumes of both objects are in a ratio of 8:1, the weight of the cube will also be in the same ratio. Therefore, the weight of the cube will be (8 * 6 kg) = 48 kg.
So, the weight of the cube made of the same metal, with sides twice as long, will be 48 kg.