ENRICHMENT ACTIVITIES (Based on Chapters 13-19)

Refer to figure and express the thickness of the inner core as a percentage of the total distance between the surface and interior most point of the earth.

The price of a commodity has increased by $20\%$. Find the reduction in the consumption of the commodity by a consumer so that there is no increase in his expenditure.

Draw the figure for Octagonal pyramid and verify Euler's formula.

Draw the figure for Square prism and verify Euler's formula.

The parallel sides of a trapezium are $10 \mathrm{cm}$ and $20 \mathrm{cm}$. Its non-parallel sides are both equal, each being $13 \mathrm{cm}$. If the area of the trapezium is $k {\mathrm{cm}}^2$, then find the value of $k$.

The dimensions of a rectangular box are in the ratio $2 : 3 : 4$ and the difference between the cost of covering it at the rate of $₹4$ and $₹4.50$ per ${\mathrm{m}}^2$ is $₹416$. Find the dimensions of the box.

A solid cube of side $12 \mathrm{cm}$ is cut into eight cubes of equal volume. What will be the side of the new cube? Also find the ratio between their surface areas.

If the diameter of the cross section of a wire is decreased by $5\%$, by what percent should its length be increased, so that the volume remains the same?