Approximately 44671

A granite monument in the shape of a pyramid with a rectangular base will be placed in the city park. The base dimensions are 60 cm and 110 cm, and the pyramid height is 220 cm. The density of granite is approximately 2800 kg/m³. Calculate the weight of the monument.

Correct answer:

m =  1355.2 kg

Step-by-step explanation:

$$\begin{gathered} a=60\text{cm}\to \text{m}=60:100\text{m}=0.6\text{m} \\ b=110\text{cm}\to \text{m}=110:100\text{m}=1.1\text{m} \\ h=220\text{cm}\to \text{m}=220:100\text{m}=2.2\text{m} \\ S=a\cdot b=\frac{3}{5}\cdot \frac{11}{10}=\frac{3\cdot 11}{5\cdot 10}=\frac{33}{50}=0.66{\text{m}}^2 \\ V=\frac{1}{3}\cdot S\cdot h=\frac{1}{3}\cdot \frac{33}{50}\cdot \frac{11}{5}=\frac{121}{250}=0.484{\text{m}}^3 \\ \rho =2800{\text{kg/m}}^3 \\ m=\rho \cdot V=2800\cdot \frac{121}{250}=\frac{2800\cdot 121}{250}=\frac{338800}{250}=\frac{6776}{5}\text{kg}=1355.2\text{kg} \end{gathered}$$

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