Question 1 :
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.
Question 2 :
A cuboidal metal of dimensions $44 cm\times 30 cm\times 15 cm$ was melted and cast into a cylinder of height $28 cm$. Find its radius.
Question 3 :
The curved surface area of a frustum cone is 250 mm$^2$. The smaller circle area is 35 mm$^2$. The total surface area is 450 mm$^2$. Find the larger circle area of a cone. 
Question 4 :
Water has to be transferred from a rectangular container with dimensions $4m\times 9m\times 10m$ into a cylindrical container that has a diameter of $6$ meters. Calculate the height of the cylinder to hold all the water from the rectangular container.
Question 5 :
The radii of the top and bottom of a bucket of slant height $45$ cm are $28$ cm and $7$ cm respectively. The curved surface area of the bucket is<br/>
Question 6 :
The frustum cone curved surface area is 389.13 $cm^3$. The upper and lower circle area of a cone is 2.5 and 6.5 cm. Find the total surface area.
Question 7 :
Find the surface area of a frustum of cone, whose larger and smaller radius is 12 and 5 m. The slant height of the cone is 20 m.
Question 8 :
The lateral surface of a cylinder is developed into a square whose diagonal is $2 \sqrt 2$ cm. The area of the base of the cylinder (in cm$^2$) is
Question 9 :
<span>The total surface area of a frustum cone is 3,250 cm$^2$. The area of larger and smaller circle is 48 and 36 cm$^2$. Find the curved surface area of a cone.</span>
Question 10 :
The volume of a frustum of a cone of height h and ends radii $r_1$ and $r_2$ is
Question 11 :
Three metallic solid cubes whose edges are 3cm, 4cm, and 1cm are melted and converted into a single cube. Find the edge of the cube so formed ?
Question 12 :
The height of the frustum cone is 30 cm. The area of the top and bottom circle of the cone is 6 cm$^2$ and 96 cm$^2$ respectively. Find its volume.
Question 13 :
<span>The larger diameter of a frustum cone is double the smaller diameter which is 6 cm. The slant height of the cone is 20 cm. What is the surface area? (Use $\pi$ = 3.14).</span>
Question 14 :
A cone is divided into two parts by drawing a plane through a point which divides its height in the ratio $1:2$ starting from the vertex and the plane is parallel to the base. Find the ratio of the volume of the two parts.
Question 15 :
A rectangular pipe of metal $16$ cm $\times 32$ cm rolled along its length and a cylinder is formed. Find the surface area of the cylinder. (Use $\pi = \dfrac{22}{7}$)<br/>
Question 16 :
The diameter of a copper sphere is $6$ cm. The sphere is melted and drawn into a wire of uniform circular cross-section which is $72$ cm long. The diameter of the wire is nearly
Question 17 :
Choose the correct alternative answer for the following question. A cone was melted and cast into a cylinder of the same radius as that of the base of the cone. If the height of the cylinder is $5\,cm$, find the height of the cone.
Question 18 :
A well $12$ m deep with diameter $3.5$ m is dug up and earth from it is evenly spread to form a  platform $10.5$ long and $8.8$m wide. Find the height of the  platfrom.
Question 19 :
The diameter of a metallic sphere is $6 cm$. It is melted and drawn into a wire of diameter $2 cm$, then the length of the wire is<br/>
Question 20 : <p>A vessel is in the form of a frustum of a cone. Its radius at top end is 12 m and the bottom end is 10 m. Its volume is 369 $ \pi m^3$. Find its height.</p>
Question 21 :
<span>The smaller diameter of a frustum cone is thrice the larger radius which is 4 in. The slant height of the cone is 13 in. What is the surface area? (Use $\pi$ = 3). </span>
Question 22 :
The diameter of a metallic sphere is $6$ cm. The sphere is melted and drawn into a wire of uniform circular cross-section. If the length of the wire is $36$ m, find the radius of its cross-section.
Question 23 :
If n coins each of diameter $1.5\ cm$ and thickness $0.2\ cm$ are melted and a right circular cylinder of height $10\ cm$ and diameter $4.5\ cm$ is made, then $n =$
Question 24 : <p><span>The frustum cone curved surface area is 230 $\pi cm^2$. The upper and lower circle area of a cone is 12.5 and 16.5 cm. Find the total surface area. (Use $\pi$ = 3.14).</span></p>
Question 25 :
A cylindrical rod whose height is $8$ times its radius is melted and cast into spherical balls of the same radius. The total number of spherical balls so formed is
Question 26 :
Find the surface area of a frustum of cone, whose larger and smaller radius is $8$ m and $4$ m. The height of the cone is $3$ cm. (Use $\pi= 3$)<br/>
Question 27 :
The volume of the greatest sphere cut off from a cylindrical wood of base radius $1$ cm and height $5$ cm is:<br/>
Question 28 :
The curved surface area of a frustum cone is 25$\pi$ mm$^2$. The larger circle area is 12$\pi$ mm$^2$. The total surface area is $350 \pi$ mm$^2$. Find the smaller circle area of a cone.
Question 29 :
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.
Question 30 :
A solid is in the shape of a cone standing on a hemisphere with b<span>oth their radii being equal to 21 m and the height of the cone is 10 m. Find the volume of the solid.</span>
Question 31 :
A right circular cone and a sphere have equal volumes. If the radius of the base of the cone is $2x$ and the radius of the sphere is $3x$, find the height of the cone in terms of $x$.
Question 32 :
<span>A iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of the base of each of cone and cylinder is 8 cm. The cylindrical part is 240 cm high and the conical part is 36 cm high. Find the weight of the pillar if $1cm^3$ of iron weighs 7.8 grams.</span>
Question 33 :
A cylinder is with in the cube touching all the vertical faces . A cone is inside the cylinder. If their heights are same with the same base . If the ratio of their volumes is x : y : z . (HCF of x , y , z = 1) , then x + y + z =
Question 34 :
A spherical ball of lead $5 \,cm$ in diameter is melted and recast into three spherical balls. The diameters of two of these balls are $2 \,cm$ and $2(14.5)^{1/3}\, cm$. Find the diameter of the third ball.
Question 35 :
What length of the solid cylinder that is $2$ cm in diameter must be taken to cast into a hollow cylinder of external diameter $12$ cm, $0.25$ cm thick, and $15$ cm long?
Question 36 :
<span>A solid toy is in the form of a right circular cylinder with a hemispherical shape of one end and a cone at the other end. Then common diameter is $4.2 cm$ and the heights of the cyndrical and conical portions are $12 cm$ and $7 cm$, respectively. Find the volume of the solid. (Take $\pi$ = 22/7)</span>
Question 37 :
A rectangular sheet of paper $22$cm long and $12$cm broad can be  curved to form the lateral surface of a right circular cylinder in two ways. Taking $\pi= \dfrac{22}{7}$. Difference in the volumes of the two cylinders thus formed is<br/>
Question 38 :
<span>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)</span>
Question 39 :
A solid is in the form of a cone mounted on a right circular cylinder both having same radii of their bases. Base of the cone is placed on the top base of the cylinder. If the radius of the base and height of the cone be 4 cm and 7 cm, respectively, and the height of the cylindrical part of the solid is 3.5 cm, the volume of the solid is equal to
Question 40 : If the radii of the circular ends of a bucket $24$ cm high are $5$ cm and $15$ cm respectively, find the inner surface area of the bucket (i.e., the area of the metal sheet required to make the bucket) <div>(Take $\pi = 3.14$)</div>
