The cup

In a measuring cup set, the cup measure is 6 cm wide. The set also contains a 1-cup measure and a cup measure, both of which are similar in shape to the cup measure. Find the width of:

a) 1/2 cup

b) the 1 cup measure

c) the 1/3 cup measure.

Correct answer:

a =  4.1838 cm
b =  8.3676 cm
c =  2.7892 cm

Step-by-step explanation:

$$\begin{gathered} V=236.588\cdot 1=236.588{\text{cm}}^3 \\ d=6\text{cm} \\ r=d/2=6/2=3\text{cm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 3^2\doteq 28.2743{\text{cm}}^2 \\ V=S_1\cdot h \\ V/2=S_1\cdot a \\ a=\frac{V}{2\cdot S_1}=\frac{236.588}{2\cdot 28.2743}=4.1838\text{cm} \end{gathered}$$

$$\begin{gathered} V=S_1\cdot b \\ b=V/S_1=236.588/28.2743=8.3676\text{cm} \end{gathered}$$

$$\begin{gathered} V/3=S_1\cdot c \\ c=\frac{V}{3\cdot S_1}=\frac{236.588}{3\cdot 28.2743}=2.7892\text{cm} \end{gathered}$$

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