$A$ wooden article was made by scooping out a hemisphere from each end of a solid cylinder,as shown in the figure. If the height of the cylinder is $10 \, cm$ and its base radius is $3.5 \, cm$,find the total surface area of the article (in $cm^2$).

$A$ well of diameter $3 \, m$ is dug $14 \, m$ deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width $4 \, m$ to form an embankment. Find the height of the embankment (in $m$). Take $\pi = \frac{22}{7}$.

$A$ cylindrical bucket,$32 \, cm$ high and with a base radius of $18 \, cm$,is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is $24 \, cm$,find the radius and slant height of the heap. [Take $\pi = \frac{22}{7}$]

$A$ pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are $15 \, cm$ by $10 \, cm$ by $3.5 \, cm$. The radius of each of the depressions is $0.5 \, cm$ and the depth is $1.4 \, cm$. Find the volume of wood in the entire stand (in $cm^3$). [Take $\pi = \frac{22}{7}$]

$A$ hemispherical depression is cut out from one face of a cubical wooden block such that the diameter $l$ of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid. $\left[\text{Use } \pi=\frac{22}{7}\right]$

$A$ spherical glass vessel has a cylindrical neck $8 \, cm$ long and $2 \, cm$ in diameter. The diameter of the spherical part is $8.5 \, cm$. By measuring the amount of water it holds,a child finds its volume to be $345 \, cm^{3}$. Check whether she is correct,taking the above as the inside measurements,and $\pi = 3.14$. (in $, cm^{3}$)