Dimensions 44551

The base of the needle is a rectangle with dimensions of 20 cm and 10 cm, its height is 15 cm. Will the plasticine we needed to model this pyramid be enough to model two pyramids with a square base of 10 x 10 cm and a height of 15 cm?

Result

x=

Yes

No

Step-by-step explanation:

$$\begin{gathered} a=20\text{cm} \\ b=10\text{cm} \\ h=15\text{cm} \\ {V}_1=\frac{1}{3}\cdot a\cdot b\cdot h=\frac{1}{3}\cdot 20\cdot 10\cdot 15=1000{\text{cm}}^3 \\ s=10\text{cm} \\ {h}_2=15\text{cm} \\ {V}_2=2\cdot \frac{1}{3}\cdot s^2\cdot h_2=2\cdot \frac{1}{3}\cdot 10^2\cdot 15=1000{\text{cm}}^3 \\ {V}_2=V_1 \\ x=1 \\ \text{ Verifying Solution: } \\ {S}_1=a\cdot b=20\cdot 10=200{\text{cm}}^2 \\ {S}_2=2\cdot s^2=2\cdot 10^2=200{\text{cm}}^2 \\ {S}_1=S_2,h=h_2=>V_1=V_2 \end{gathered}$$

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