** **** **
**Level 2 **
**11)**** ****The interior of the building is in the form of cylinder of
diameter 4.3 m and height 3.8 m surmounted by a cone whose vertical angle is a
right angle. Find the area of the surface and the volume of the building. Take
π= 3.14 **

** Ans [****71.83 m**^{2 }, 65.55 m^{3}**]**

**12)**** ****A solid composed of a cylinder
with hemispherical ends. If the whole length of the solid is 104 cm
and the radius of each hemispherical ends is 7 cm, find the cost of
polishing its surface at the rate of Rs 10/dm**^{2}. **[Rs 457.60]**

**13) ****A toy is in the form
of a hemisphere surmounted by a right circular cone of the same base
radius as that of the hemisphere. If the radius of the base of the cone is
21cm and its volume is 2/3 of the volume of the hemisphere. Calculate
the height of the cone and the surface area of the
toy. ****[28
cm, 5082 cm**^{2}]

**14) ****The perimeters of the
ends of a frustum are 48 cm and 36 cm. If the height of the frustum be 11 cm,
find its
volume. ****[1554 cm**^{3}]

**15) ****The height of the
cone is 30 cm. A small cone is cut off at the top by the plane parallel to the
base . If its volume be 1/27 of the volume of the given cone, at
what height above the base is the section
made. ****[20 cm]**

**16)**** ****The height of the right circular cone is trisected by two
planes drawn parallel to the base. Show that the volumes of the three
portions starting from the top are in the ratio 1: 7 : 19**

**17)****
A shuttle cock used for playing badminton has the shape of a frustum of cone
mounted on a hemi-sphere. The external diameter of the frustum are 5 cm and 2
cm, the height of the entire shuttle cock is 7 cm. Find its external
surface area. ****[74.26 cm**^{2}]** **

**18)****
A right angled triangle whose sides are 3cm, 4cm and 5cm is revolved about the
sides containing the right angle in two ways. Find the difference in volumes of
the two cones so formed. Also, find their curved surfaces.**

**19)**** ****The diameters of internal and external surfaces of a hollow
spherical shell are 6 cm and 10 cm respectively. If it is melted
and recast into a solid cylinder of length 8/3 cm , find the diameters of the
cylinder. ****[14 cm]**

**20) ****A
solid cone of base radius 10 cm is cut into 2 parts through the mid-points of
its heights ,by a plane parallel to its base. Find the ratio in the volumes of
two parts of the cone.**

** **** **** **** **
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