Question 1 :
Find the volume of a frustum cone, whose baseand upper area of a circle is 20 and 80 $m^2$. The height of the cone is 45.5 m.
Question 2 :
Identify the volume of largest cone which can be carved out from a cube of edge '$a$' cm.
Question 3 :
A cylindrical box of radius <b>5 </b>cm contains <b>10</b> solid spherical balls each of radius <b>5</b> cm. If the topmost ball touches the upper cover of the box, then the volume of the empty space in the box is :
Question 4 : <p>If the radii of the circular ends of a conical glass are $15$ and $9$ cm whose slant height is 35 cm. Find the surface area of the glass? (Use $$\pi $ = $3$)</p>
Question 5 :
Find the curved surface area of a frustum cone whose larger and smallerradius is 12 and 8 cm. The slant height is 24 cm. (Use $\pi$ = 3.14)
Question 6 :
A solid in shape of a frustum is 21 cm high. Its radius of top is 10 cm and diameter of bottom is 30 cm. The volume of the solid is
Question 7 :
A shuttle cock used for playing badminton has the shape of the combination of<br>
Question 8 :
A cone of height $7$ cm. and base radius $3$ cm. is carved from a rectangular block of wood of dimensions $10 cm. \times 5 cm. \times 2$ cm. The percentage of wood wasted is
Question 9 :
The shape formed by rotating a right triangle about its height is
Question 10 :
Find the volume of the frustum cone whose base and topradius is 20 ft and 10 ft respectively. The height of the cone is 300 ft. (Use $\pi$= 3).
Question 11 :
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes.<br/>
Question 12 :
A solid sphere of radius $6\;cm$ is melted and recast into small spherical balls each of diameter $1.2\;cm$. Find the number of balls, thus obtained.
Question 13 :
A bucket is in the shape of the frustum with the top and bottom circle area is $250$ and $150$ $m^2$. The height of the bucket is $27$ m. Find the volume.
Question 14 :
A metallic solid cone is melted and cast into a cylinder of the same base as that of the cone. If the height of the cylinder is $7\;cm$, what was the height of the cone?
Question 15 :
Find the capacity of a glass which is in the shape of frustum of height $14$cm and diameters of both circular ends are $4$cm and $2$cm.
Question 16 :
How many cubes of $10\ cm$ edge can be put in a cubical box of $1\ m$ edge?
Question 17 :
The base and top diameter of a cone is 1.2 mm and 0.5 mmrespectively. The height of the cone is 24 mm. What is the volume of frustum ofa cone? (Use $\pi$= 3).
Question 18 : <p>The slant heightof a frustum of a flower pot is 2 mm and the perimeters of its circular endsare 12 mm and 4 mm. Find the curved surface area of the flower pot.</p>
Question 19 : <p>The slant heightof a frustum of a drum is 12 ft and the perimeters of its circular ends are 10ft and 2 ft. Find the curved surface area of the drum.(Use $\pi$ = 3.14)</p>
Question 20 :
The volume of a frustum of cone is calculated by using the formula ______.
Question 21 :
A spherical iron ball of radius $9\;cm$ is melted and recast into three spherical balls. If the radius of two balls be $1\;cm\;and\;8\;cm$, find the radius of the third ball.
Question 22 :
If a solid of one shape is converted to another, then the volume of the new solid<br>
Question 23 :
A friction clutch is in the form of a frustum of  cone. The radius of the ends bring $16$ cm and $10$ cm. Find its curved surface area. The slant height of the friction clutch is $12$ cm.
Question 24 :
How many bricks, each measuring $25\ cm\times 11.25\ cm\times 6\ cm$, will be needed to build a wall $8\ m$ long, $6\ m$ high and $22.5\ cm$ thick?
Question 25 :
If$ \displaystyle S_{1} $ and $\displaystyle S_{2} $ be the whole surface of a sphere and the curved surface of the circumscribed cylinder then$ \displaystyle S_{1} $ is equal to
Question 26 :
During conversion of a solid from one shape to another, the volume of the new shape will<br>
Question 27 :
A right circular cone is 84 cm high The radius of the base is 350 m Find the curved surface area
Question 28 :
A solid metallic cube with edge $44$cm is melted and recast to produce small spherical balls of radius $2$cm. Then, _______ balls are produced.
Question 29 :
Assertion: No. of spherical balls that can be made out of a solid cube of lead whose edge is 44 cm, each ball being 4 cm. in diameter, is 2541
Reason: Number of balls $=$(Volume of one ball)/(Volume of lead)
Question 30 :
The dimensions of a room are $10\ m\times 8\ m\times 3.3\ m$. How many men can be accommodated in this room if each man requires $3m^3$ of space?
Question 31 :
Volume of a bucket 84 cm high, diameter of top as 40 cm and radius of bottom as 10 cm is
Question 32 :
The radii of the ends of a bucket $30cm$ high are $21cm$ and $7cm$. Find its capacity in litres and the amount of sheet required to make this bucket.
Question 33 :
The diameterof oneof the bases of atruncated cone is $100 $mm. If the diameterof this base is increased by $21 \%$such that it still remains a truncated cone with the height and the other base unchanged, the volume also increasesby $21 \% $.The radius the other base (in mm) is
Question 34 :
The diameters of the two circular ends of the bucket are $44 $ cm and $24 $ cm. The height of the bucket is $35$ cm. The capacity of the bucket is<br/>
Question 35 :
Find the curved surface area of frustum coneradii 0.2 and 3.2 cm and a slant height 5 cm. (Use $\pi$ = 3.14).
Question 36 :
STATEMENT - 1: The slant height of frustum of a cone is 4 cm. and perimeters of its circular ends are 18 cm. and 6 cm. then the curved surface area is 48 sq. cm.<br/>STATEMENT - 2: Curved surface area of frustum $ = \pi (r_1+r_2) $, where $r_1$ and $r_2$ are radii of the frustum and $l$ is a slant height.<br/>
Question 37 :
The area of top and bottom faces of a frustum are 16 $\displaystyle cm^{2}$ and 36 $\displaystyle cm^{2}$ .If the frustum is 30 cm high its volume is
Question 38 :
A frustum of a right circular cone of height $16$ cm with radii of its circular ends as $8$ cm and $20$ cm has its slant height equal to:<br/>
Question 39 :
Thevolume of the frustum of a cone is 54 cm$^3$ and its height is 6 cm, bottomradius, R = 1 cm. Find its top radius, r. (Use $\pi$= 3).
Question 40 :
A sphere of radius $r$ is inscribed inside a cube. The volume enclosed between the cube and the sphere is :
Question 41 :
A dish in the shape of a frustum of a cone has a height of $6$cm. Its top and its bottom have radii of $24$cm and $16$cm respectively. Find its curved surface area. ( in $\displaystyle cm^{2}$)
Question 42 :
The interior of a building is in the form of a right circular cylinder of a diameter 4.2 m and height  4 m, surmounted by a cone. The vertical height of the cone is 2.1 m. Find the outer surface area and volume of the building.(Take $\pi$ = 22/7)
Question 43 :
A cube whose volume is $1/8$ cubic centimeter is placed on top of a cube whose volume is $1{cm}^{3}$. The two cubes are then placed on top of a third cube whose volume is $8{Cm}^{3}$. The height of the stacked cubes is
Question 44 :
A balloon is in the form of right circular cylinder of radius $1.5 m$ length $4 m$ and is surmounted by hemi spherical ends. If the radius is increased by $0.01 m$ & the length by $0.05m$ , the percentage change in the volume of balloon is $abcd\% $, then the value of abcd must be ?<br/>
Question 45 :
A solid sphere of radius 6 mm is melted and then cast into small spherical balls each of radius 0.6 mm. Find the number of balls thus obtained.
