A note for the parent

What your child had to do in this Surface Areas and Volumes problem

This was not a watch-and-copy exercise. The student had to make 7 small mathematical decisions and correct any wrong turns before moving forward.

The skill being built

Reasoning, not answer recognition

Volume is conserved on melting: shell volume

=

cone volume. The shell is the outer ball minus the inner ball,

\dfrac{4}{3}\pi(R^3 - r^3)

with

R^3 - r^3 = 64 - 8 = 56

, so

\dfrac{16}{3}\pi h = \dfrac{224}{3}\pi

and

h = 14

cm.

The mistake we watch for

A wrong answer is useful evidence

Subtracting the radii first and cubing the difference:

(4 - 2)^3 = 8

instead of

4^3 - 2^3 = 56

. That gives

16h = 32

and the wrong height

h = 2

cm.

What happens when a step goes wrong?

The choice is crossed out

The app does not pretend the mistake did not happen.

The reason is explained

The child sees the exact misconception behind that choice.

The child tries again

The app guides, but the student still makes the next decision.

If this teaching style helps

Let your child keep learning this way

Create a free account to save progress and explore the Linear Equations chapter with no expiry. Get the Board Prep Pass for the complete learning path across all 14 chapters.

Let my child continue Try the problem myself

₹999 one-time. All 14 chapters. Access until 31 March 2027. Linear Equations stays free.