$A$ 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 $\pi = \frac{22}{7}$]

Mayank made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end (see figure). The height of the cylinder is $1.45\, m$ and its radius is $30\, cm$. Find the total surface area of the bird-bath in $m^2$. (Take $\pi = \frac{22}{7}$)

Rachel,an engineering student,was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is $3\, cm$ and its total length is $12\, cm$. If each cone has a height of $2\, cm$,find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.) Unless stated otherwise,take $\pi = \frac{22}{7}$. (in $cm^3$)

$A$ 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 $\pi = \frac{22}{7}$]

$A$ solid consisting of a right circular cone of height $120\, cm$ and radius $60\, cm$ standing on a hemisphere of radius $60\, cm$ is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder,if the radius of the cylinder is $60\, cm$ and its height is $180\, cm$. [Take $\pi = \frac{22}{7}$.] (in $m^3$)

How many silver coins,$1.75 \,cm$ in diameter and of thickness $2 \,mm$,must be melted to form a cuboid of dimensions $5.5 \,cm \times 10 \,cm \times 3.5 \,cm$? [Take $\pi = \frac{22}{7}$]