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A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, the edge of the third smaller cube is?

The base radius and height of a right circular cylinder is in the ratio of 1:7. If the volume is 176 cm$^3$, the total surface area of the right circular cylinder is:

A Swimming pool was constructed for swimmers with 18 meter wide and 24 meter long is 4 meter deep on shallow side and 8 meter deep on the deeper side. It's volume for average depth is:

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A drainage tile is a cylindrical shell 21cm long. The inside and outside diameters are 4.5 cm and 5.1 cm, respectively.

What is the volume of clay required for making a tile?

Consider the surface area of the following:

(A) A cube having each side as 6 cm.

(B) A cylinder with a diameter of base 14 cm and length 80 cm.

(C) A cone of diameter 14 cm and a slant height of 10 cm.

(D) A sphere of radius 10.5 cm.

The surface area of these in decreasing order are:

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The ratio of the diameter and height of the right circular cylinder is 4 : 3. If the diameter of the cylinder is reduced 25 %, then its total surface area is reduced to 318.5π m². What is the circumference of the base of the cylinder?

If a cone and sphere have equal radii and volumes, then determine the ratio of the diameter of the sphere to the height of the cone?

If the ratio of the radii of the sphere and hemisphere is √3:2, then determine the ratio of their total surface area?

A solid, metallic right circular cone of radius 7 cm and height 3 cm is melted into three cubes. If the sides of two cubes are 3 cm and 5 cm, then the side of the third cube will be how much?

A solid sphere of radius 15 cm is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 9 cm and its height is 100 cm, find the uniform thickness of the cylinder.

A flask in the shape of a right circular cone of height 36 cm is completely filled with tea. The tea is then poured into another right circular cylindrical flask whose radius is two-third of the radius of base of the circular cone. Then, the height of the tea in the cylindrical flask is

The ratio of the radius and height of a cone is 3:4. Its volume is $37\frac{5}{7}$ cm³. The slant height of the cone is

If the length of a cuboid is increased by 20% and its breadth is decreased by 20%, then the volume of cuboid

If a metallic rod of 10 cm length and 2 cm radius is stretched into a wire of 40 m length having uniform thickness, then find the radius of the stretched wire.

If the slant height of a cone is decreased by 15 percent and the radius of its base is increased by 20 percent, then by what percent will its curved surface area change?

A sphere of maximum volume is 'cut out' from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut-out sphere is:

A right circular metal cone (solid) is 42 cm high and its radius is $\frac{21}{2}$ cm. It is melted and recast into a sphere. Then the radius of the sphere will be:

If the areas of adjacent faces of a cuboid (rectangular prism) are in the ratio of 2: 3: 5 and its volume is 900 cm³, then the length of the longest side is

If the radius of a sphere is increased by 50%, find the percent increase in surface area.

How many meters of cloth 6 metre wide will be required to make a conical tent, the radius of whose base is 21m and height is 20m?

Find the values and arrange in increasing order:

(A) If each edge of a cube is increased by 20%, then the percentage increase in its volume is:

(B) If the radius of a cylinder is increased by 20%, while height increase 10%, then the percentage increase in the volume of the cylinder

(C) If each edge of a cube is increased by 20%, then the percentage increase in its surface area is:

(D) If the radius of a sphere is increased by 10%, then the percentage increase in its volume is:

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The areas of three adjacent faces of a cuboidal box are 96 cm², 48 cm² and 72 cm², respectively. The volume of the box is

The base radius of a cone is 21 cm and the height is 28cm, then which of the following is/are correct?

(A) Slant height = 35 cm

(B) Slant height = 33 cm

(C) Volume = 12936 cm³

(D) Curved Surface Area = 2310 cm²

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In what ratio are the volumes of a cylinder, a cone and a sphere, if each has the same diameter and the same height?

Three spherical balls of radius 2 cm, 4 cm, and 6 cm are melted to form a new spherical ball. In this process, there is a loss of 25% of the material. What is the radius (in cm) of the new ball?

A cylindrical jar having a base of radius 15 cm, is filled with water up to a height of 20 cm. If a solid iron spherical ball of radius 10 cm is dropped in the jar to submerge completely in the water, then the increase in the level of water is:

The ratio of radii of two right circular cylinders (A and B) is 2:3. The ratio of volumes of the cylinders A and B is 9:7, then what is the ratio of the heights of the cylinders A and B?

$V_1, V_2, V_3$ and $V_4$ are the volumes of four cubes of side lengths x cm, 2x cm, 3x cm and 4x cm respectively. The following statements regarding these volumes are given below.

(A) $V_1 + V_2 + 2V_3 < V_4$

(B) $V_1 + 3V_2 > V_3 + V_4$

(C) $2(V_1 + V_3) + V_2 = V_4$

(D) $V_1 + 4V_2 + V_3 < V_4$

Which of these statements is/are correct?

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