Calculate 67794

Calculate the volume of the cuboid in the given unit if you know the lengths of its edges.
A) a = 20 cm, b = 3 cm, c = 7 cm, (length)
B) a = 10 mm, b = 8 mm, c = 9 mm, (ml)
C) a = 30 cm, b = 5 cm, c = 8 cm, (l)
D) a = 300 mm, b = 4 m, c = 7 dm, (hl)

Correct answer:

A =  4.2 dl
B =  0.72 ml
C =  1.2 l
D =  8.4 hl

Step-by-step explanation:

$$\begin{gathered} a=20\text{cm} \\ b=3\text{cm} \\ c=7\text{cm} \\ {V}_1=a\cdot b\cdot c=20\cdot 3\cdot 7=420{\text{cm}}^3 \\ A=V_1\to \text{dl}=V_1:100\text{dl}=420:100\text{dl}=4.2\text{dl}=4.2\text{dl} \end{gathered}$$

$$\begin{gathered} a_2=10\text{mm}\to \text{cm}=10:10\text{cm}=1\text{cm} \\ {b}_2=8\text{mm}\to \text{cm}=8:10\text{cm}=0.8\text{cm} \\ {c}_2=9\text{mm}\to \text{cm}=9:10\text{cm}=0.9\text{cm} \\ {V}_2=a_2\cdot b_2\cdot c_2=1\cdot 0.8\cdot 0.9=\frac{18}{25}=0.72{\text{cm}}^3 \\ B=V_2\to \text{ml}=V_2\cdot 1\text{ml}=0.72\cdot 1\text{ml}=0.72\text{ml}=0.72\text{ml} \end{gathered}$$

$$\begin{gathered} a_3=30\text{cm} \\ {b}_3=5\text{cm} \\ {c}_3=8\text{cm} \\ {V}_3=a_3\cdot b_3\cdot c_3=30\cdot 5\cdot 8=1200{\text{cm}}^3 \\ C=V_3\to \text{l}=V_3:1000\text{l}=1200:1000\text{l}=1.2\text{l}=1.2\text{l} \end{gathered}$$

$$\begin{gathered} a_4=300\text{mm}\to \text{m}=300:1000\text{m}=0.3\text{m} \\ {b}_4=4\text{m} \\ {c}_4=7\text{dm}\to \text{m}=7:10\text{m}=0.7\text{m} \\ {V}_4=a_4\cdot b_4\cdot c_4=0.3\cdot 4\cdot 0.7=\frac{21}{25}=0.84{\text{m}}^3 \\ D=V_4\to \text{hl}=V_4\cdot 10\text{hl}=0.84\cdot 10\text{hl}=8.4\text{hl}=8.4\text{hl} \end{gathered}$$

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