Dimensions 5989

The owners of the ornamental garden decided to beautify the entrance to the garden with two granite plinths composed of a prism and a sphere. The sphere has a diameter of 56 cm; the prism has dimensions of 60 cm, 60 cm, and 150 cm. How much will the owners pay for the pedestals if 1 dm³ of granite weighs 2.75 kg and 10 kg of granite costs 35 euros?

Correct answer:

x =  12165.0822 Eur

Step-by-step explanation:

$$\begin{gathered} a=60/10=6\text{dm} \\ b=60/10=6\text{dm} \\ c=150/10=15\text{dm} \\ D=56/10=\frac{28}{5}=5.6\text{dm} \\ {V}_1=a\cdot b\cdot c=6\cdot 6\cdot 15=540{\text{dm}}^3 \\ r=D/2=\frac{28}{5}/2=\frac{28}{5\cdot 2}=\frac{28}{10}=\frac{14}{5}=2.8\text{dm} \\ {V}_2=\frac{4}{3}\cdot \pi \cdot r^3=\frac{4}{3}\cdot 3.1416\cdot 2.8^3\doteq 91.9523{\text{dm}}^3 \\ V=V_1+V_2=540+91.9523\doteq 631.9523{\text{dm}}^3 \\ m=2.75\cdot V=2.75\cdot 631.9523\doteq 1737.8689\text{kg} \\ {x}_1=m/10\cdot 35=1737.8689/10\cdot 35\doteq 6082.5411\text{eur} \\ x=2\cdot x_1=2\cdot 6082.5411=12165.0822\text{Eur} \end{gathered}$$

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