Question

If the radius of a sphere is increased by 12%, then the percentage increase in volume is
A) 80
(B) 20.5%
(C) 40.5
(D) 609​

Answer 1

Answer:

40.5%

Step-by-step explanation:

Let the initial radius be 1(or suppose a sphere of unit radius).

That time, using volume = (4/3)πr³,

volume = (4/3)π(1)³ = (4/3)π

When radius is increased by 12%, means

new radius = 1 + 12% of 1

= 1 + (12/100) x 1

= 1.12

Volume = (4/3)π(1.12)³ ≈ (4/3)π(1.405)

% increase = (new - old)/old x 100%

= [(4/3)π(1.405) - (4/3)π]/(4/3)π x 100%

= (4/3)π[1.405 - 1] / (4/3)π x 100%

= (1.405 - 1) x 100%

= 0.405 x 100%

= 40.5 %

Answer 2

Answer:

$\huge \fbox {40.5}$

Let the initial radius of circle be 1 .

Thus that time using volume formula = (4/3) πr³

Volume = (4/3) π(1)³ = 4/3 π

Then the radius is increased by 12%

So, new radius = 1 + 12% of 1

We know that 1 percent = 1/100

So , 1 + 12/100 × 1

= 1.12

Increase percent = (new - old) / old × 100

Increase percent = [(4/3) π (1.405) - (4/3) π] /(4/3)π × 100%

Increase percent = (4/3)π [1.405-1] / 4/3 π × 100%

Increase percent = (1.405-1) × 100%

Increase percent = 0.405 × 100

Increase percent = 40.5

Extra information

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$value \: of \: \huge \pi \: = \frac{22}{7}$

$area \: of \: circle \: = \pi {r}^{2}$