Question

Calculate the volume of a rectangular block in cubic meter, cubic cm. and cubic ft. that has length of 33 cm and has a width of .89ft and height of 0.20 meter.

Answer 1

Task:

Calculate the volume of a rectangular block in cubic meter, cubic cm. and cubic ft. that has length of 33 cm and has a width of .89ft and height of 0.20 meter.

Solution:

The volume of a rectangular block is

$$V(\text{cm}^3) = a(\text{cm}) \cdot b(\text{cm}) \cdot c(\text{cm})$$

a(cm) – length of the block

b(cm) - width of the block

c(cm) – height of the block

For the calculations we should remember that

$$1\,\text{m} = 100\,\text{cm} = 3.2808\,\text{ft}$$ $$33\,\text{cm} = 0.33\,\text{m} = 1.083\,\text{ft}$$ $$0.89\,\text{ft} = 0.2713\,\text{m} = 27.13\,\text{cm}$$ $$0.20\,\text{m} = 20\,\text{cm} = 0.6562\,\text{ft}$$

Volume in $\text{m}^3$ is

$$V(\text{m}^3) = 0.33 \cdot 0.2713 \cdot 0.20 = 1.8 \cdot 10^{-2}\,\text{m}^3$$

Volume in $\text{cm}^3$ is

$$V(\text{cm}^3) = 33 \cdot 27.13 \cdot 20 = 1.8 \cdot 10^4\,\text{cm}^3$$

Volume in $\text{ft}^3$ is

$$V(\text{ft}^3) = 1.083 \cdot 0.89 \cdot 0.6562 = 0.63\,\text{ft}^3$$

Answer: $V = 1.8 \cdot 10^{-2}\,\text{m}^3 = 1.8 \cdot 10^4\,\text{cm}^3 = 0.63\,\text{ft}^3$