The capacity of the vessel is 150 cm³
Step-by-step explanation:
The given is:
We need to find the capacity of the vessel
Assume that the base area of the cuboidal vessel is x cm²
The volume of a cuboid = base area × height
∵ The base area of the cuboidal vessel = x cm²
∵ Its height = 12 cm
∴ The volume of the vessel = x × 12 = 12x cm³
∵ The height of the water in the vessel = 4 cm
- The water takes the shape of the vessel, then base area of
water is equal to the base area of the vessel
∵ The volume of the water = base area of the vessel × its height
∴ The volume of the water = x × 4 = 4x cm³
∵ 100 cm³ of water is filled in the vessel
∵ The water is reached to the brim
∴ The volume of the vessel = the volume of the water
∵ The volume of the vessel = 12x cm³
- The volume of the water in the vessel is the sum of 4x and 100
∵ The volume of the water = (4x + 100) cm³
∴ 12x = 4x + 100
- Subtract 4x from both sides
∴ 8x = 100
- Divide both sides by 8
∴ x = 12.5 cm²
Substitute the value of x in the volume of the vessel
∵ The volume of the vessel = 12x
∴ The volume of the vessel = 12(12.5)
∴ The volume of the vessel = 150 cm³
- The volume of the vessel = the capacity of the vessel
∴ The capacity of the vessel = 150 cm³
The capacity of the vessel is 150 cm³
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