Question

The volume of a cube is increased by 700 % . By how much will its surface area increase?

Answer 1

Answer:

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Step-by-step explanation:

The volume of a spherical balloon has increased by 700%. What is the percentage increase in its surface area?

The volume and surface area of a sphere are V=4πr33 and S=4πr2 respectively.

Let the subscripts 1 and 2 indicate the initial and final values.

The volume has increased by 700%.

⇒ The new volume is 8 times the old volume.

⇒V2V1=8.

⇒4πr3234πr313=8⇒r32r31=8.

⇒r22r21=(8)2/3=4.

⇒S2S1=4πr224πr22=r22r22=4.

⇒S2−S1=3S1.

⇒ The increase in surface area is 300%

Answer 2

Step-by-step explanation:

The volume and surface area of a sphere are V=4πr33 and S=4πr2 respectively.

Let the subscripts 1 and 2 indicate the initial and final values.

The volume has increased by 700%.

⇒ The new volume is 8 times the old volume.

⇒V2V1=8.

⇒4πr3234πr313=8⇒r32r31=8.

⇒r22r21=(8)2/3=4.

⇒S2S1=4πr224πr22=r22r22=4.

⇒S2−S1=3S1.

⇒ The increase in surface area is 300%.