** **** **

**QUESTION 9**

**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}**]**

**UESTION 10**

**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]**

**QUESTION 11**

**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}]

**QUESTION 12**

**What length of the solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of length 16 cm, external diameter 20 cm and thickness 2.5 mm. ****[79 cm]**

**QUESTION 13**

**A well of diameter 2 m is dug 14m deep. The earth taken out it has been spread evenly all around it to form an embankment of height 40 cm. Find the width of embankment. **** ****[5 m]**

**QUESTION 14**

**2.2 dm**^{3} of brass is to be drawn into a cylindrical wire 0.25 cm in diameter . Find the length of the wire. **[448 m]**

**QUESTION 15**

**How many spherical bullets each of 5 cm in diameter can be cast from a rectangular block of metal 11 dm x 1 m x 5 dm. ****[8400**** bullets]**

**QUESTION 16**

**An agriculture field is in the form of a rectangle of length 20m and width 14m. A 10 m deep well of diameter 7m is dug in a corner of the field and the earth taken out of the well is spread evenly over the remaining part of the field. Find the rise in its level. [1.594 cm]**

** Hint [Area of field - 𝝅r**^{2} ] x h = Volume of the earth taken out from the well ]

**QUESTION 17**

**50 circular plates each of diameter 14 cm and thickness 0.5 cm are placed one above the other to form a right circular cylinder. Find the total surface area ? ****[1408 cm**^{2}]

**QUESTION 18**

**Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9 cm ? **** ****[190.93 cm**^{3}]

**QUESTION 19**

**Prove that the surface area of the sphere is equal to the curved surface of circumscribed cylinder.**

**QUESTION 20**

**The radius of the solid iron sphere is 8 cm. Eight rings of iron plate of external radius 20/3 cm and thickness 3cm are made by melting this sphere. Find the internal diameter of each ring. ****[4 cm****]**

**A conical vessel of radius 6 cm and height 8 cm is completely filled with water. ****A sphere is lowered into the water and its size is such that when it touches the sides**** it is just immersed as shown in the figure. What fraction of the water flows out. ****[Ans 3 : 8 ]**

**QUESTIONS DELETED FROM CBSE SYLLABUS**

**QUESTION 21**

**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**

**QUESTION 22**

**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}]** **

**QUESTION 23**

**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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