Question

The Money required to paint a cube of volume V is x Rs. We have another cube with volume 64V. How much money do we need to paint this new cube?


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Answer 1

Answer:

answer=64x rupees

Step-by-step explanation:

V=x rupees

then 64V=64x rupees

Answer 2

Given:

Volume of 1 cube = V units³

it costs Rs x to paint the cube.

To Find:

Find the cost of painting another cube with volume = 64V units³

Solution:

Find the length of the original cube:

$\text{Volume} = \text{Length}^3$

$\text{Length}^3 = V$

$\text{Length} = \sqrt[3]{V}$

Find the length of the other cube:

$\text{Volume} = \text{Length}^3$

$\text{Length}^3 = 64V$

$\text{Length} = \sqrt[3]{64V}$

$\text{Length} = 4\sqrt[3]{V}$

Find the ratio of the two areas:

$\dfrac{\text{Area}_1}{\text{Area}_2} = \bigg(\dfrac{\text{Length}_1}{\text{Length}_2} \bigg)^2$

$\dfrac{\text{Area}_1}{\text{Area}_2} = \bigg(\dfrac{\sqrt[3]{V} }{4\sqrt[3]{V} } \bigg)^2$

$\dfrac{\text{Area}_1}{\text{Area}_2} = \bigg(\dfrac{1}{4} \bigg)^2$

$\dfrac{\text{Area}_1}{\text{Area}_2} = \dfrac{1}{16}$

Find the cost of painting:

$\text{Area}_1 : \text{Area}_2 = 1. 16$

$\text{Area}_1 = \text{Rs }x$

$\text{Area}_2 = 16 (x)$

$\text{Area}_2 = \text{Rs }16x$

Answer: The cost o paint the other cube is Rs 16x