Question

In a size transformation, the area of the image of an object of area 6 mºis 37.5 cm². Calculate:The scale factor.il. The volume of an object, if the volume of its image is 360 cm'.1.​

Answer 1

Volume of the object is 0.005625 cm³

Step-by-step explanation:

Since scale factor of the sides = $\sqrt{\frac{\text{Area of the Image}}{\text{Area of the object}} }$

= $\sqrt{\frac{60000}{37.5}}$

= $\sqrt{1600}=40$

Now volume of the image = 360 cm³

By the formula Scale factor = $\sqrt[3]{\frac{\text{Volume of the image}}{\text{Volume of the object}} }$

40 = $\sqrt[3]{\frac{360}{\text{Volume of the object}}}$

(40)³= $\frac{360}{V}$

V = $\frac{360}{(40)^{3}}$

Volume of the object = 0.005625 cm³

Therefore, volume of the object is 0.005625 cm³

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