Certainly! Let’s solve each part step-by-step.
### Part (a)
Given the volume of a cube is 512 cm³, we need to find the side length of the cube.
The formula for the volume of a cube is:
[tex]\[ V = s^3 \][/tex]
where [tex]\( V \)[/tex] is the volume and [tex]\( s \)[/tex] is the side length of the cube.
We are given [tex]\( V = 512 \)[/tex] cm³. To find [tex]\( s \)[/tex], we take the cube root of the volume:
[tex]\[ s = \sqrt[3]{512} \][/tex]
Now, calculate the cube root of 512:
[tex]\[ 512 = 8 \times 64 = 8 \times 8^2 = 8^3 \][/tex]
Thus,
[tex]\[ s = 8 \, \text{cm} \][/tex]
So, the side length of the cube is 8 cm.
### Part (b)
Given the capacity of a cubical water tank is 343000 cm³.
(i) What is the volume of the tank?
Since the tank is cubical, the capacity and the volume are the same. Therefore, the volume of the tank is:
[tex]\[ \text{Volume of the tank} = 343000 \, \text{cm}³ \][/tex]
(ii) How high is the tank?
Given the volume of the tank, we need to find the side length (or height, since it’s a cube) of the tank. We use the same volume formula for a cube:
[tex]\[ V = s^3 \][/tex]
We are given [tex]\( V = 343000 \)[/tex] cm³. To find [tex]\( s \)[/tex], we take the cube root of the volume:
[tex]\[ s = \sqrt[3]{343000} \][/tex]
Now, calculate the cube root of 343000. Note that this can be broken down for easier calculation if necessary, but let’s directly find the cube root:
[tex]\[ s \approx 70 \][/tex]
So, the approximate side length or height of the tank is 70 cm.
### Summary
- Part (a): The side length of the cube is 8 cm.
- Part (b):
- (i) The volume of the tank is 343000 cm³.
- (ii) The height (or side length) of the tank is approximately 70 cm.
