The height of a cone is 30 cm. The cone is cut parallel to its base, such volume of the cone and frustum so formed is in the ratio 13.5 : 49. Find at which height from the base the cone is cut?

The difference between the outside and the inside surface area of a cylindrical pipe 14 cm long is 44 cm². The pipe is made of 99 cm³ of metal. If R is the outer radius and r is the inner radius of the pipe, then what is (R + r) equal to?

The volume of a right circular cone is 1078 cm³. Find the total surface area of the cone if its height is 21 cm. (Use π = 22/7)

The curved surface area of a solid metallic right circular cylinder is 1792π cm^2, and its base radius is 32 cm. It is me recast into 42 solid spherical balls of equal radius. What is the surface area (in sq cm) of a ball?

The cost of polishing the total surface area of a solid cone at Rs 0.50/sq cm is Rs 5632, and the circumference of its base is 176 cm. What is the height of the cone?

A glass cylinder with a diameter of 20 cm has water to a height of 9 cm. A metal cube of 8 cm edge is immersed in it completely. Calculate the height (correct to 1 decimal place) by which the water will rise in the cylinder (by taking π = 3.142).

The cost of polishing the total surface area of a solid cone at ₹0.50 /sq cm is ₹5632, and the circumference of its base is 176 cm. What is the height of the cone?

A cylinder is completely filled with water. A certain number of cylindrical bullets of diameter 1.4 cm and height 3 cm are gradually immersed into water in the cylinder. From the cylinder 5.544 litres of water oveflows which is collected in a vessel. How many bullets were immersed into the cylinder? (Take \(\pi=\frac{22}{7}\))

If the sum of slant height, height, and radius is (9 + 9√3) cm, then what is the volume of the cone?

The angle at the vertex of a conical body is 90°. What is the ratio of the radius of the conical body to its slant height?

The outer surface of a sphere having a diameter 10 m is painted at the rate of Rs. \(\frac{80}{\pi}\) per m² . What is the cost of painting?

(i) the total surface area of the frustum.

A solid metallic sphere of radius 6 cm is melted and recast into spherical balls of radius 3 cm. The number of spherical balls thus obtained is:

A hollow cylindrical tube made of plastic is 3 cm thick. If the external diameter is 20 cm and length of the tube is 49 cm, find the volume of the plastic.

(ii) the ratio of the areas of the two circular ends:

Two cylinders have the radii of their bases in the ratio 4 : 5 and their heights are in the ratio 5 : 7. Find the ratio of their curved surface areas.

A solid cone with curved surface area twice its base area has slant height of 6√3 cm. Its height is :

The circumference of the base of the cylindrical vessel is 154 cm and its height is 49 mm. How many litres of water can it hold? (correct to three places of decimals, use \(\pi = \frac{22}{7}\))

A well with 14 cm radius is dug 23 cm deep. Find the volume of the earth taken out of it.

The curved surface area of a cone is 2200 cm² and its radius is 28 cm, what is the slant height (in cm) of the cone?\(\big(Use\pi=\frac{22}{7}\big)\)

If three spheres of radius 75 cm, 60 cm and 45 cm are melted into one big sphere, then the radius of the big sphere is:

Find the curved surface area of a cone whose radius is 13 cm and slant height is 21 cm. (use π = 22/7 and CSA in cm²)

To have a surface area of 9π square units of a ball, what should be the radius (in units) of the ball?

Find the curved surface area of the hemisphere (in cm²) whose radius is 60 cm and π = 3.14.

A cylindrical candle, 14 cm in diameter and length 2 cm is melted to form a cuboid candle of dimensions 7 cm x 11 cm x 2 cm. How many cuboidal candles can be obtained?

Find the volume of the largest possible sphere circumscribed by a cube with an edge of 7 cm.

If the radius and height of a right circular cylinder are 21 cm and 5 cm, respectively, then the total surface area of cylinder is (use \(\pi =\frac{22}{7} \)):

A rectangle of length, 14 cm and breadth, 7 cm is rotated about its shorter side to form a cylinder. What is the volume (in cm³) of the cylinder so generated? (Take π = \(22\over7\))

The material of a solid right circular cylinder is converted into the shape of a solid cone of equal radius. If the height of the cylinder was 4.5 cm, then the height of the cone is:

If the surface area of the sphere is 616 cm², then the radius of the sphere is equal to:

What is the volume of the cone with a radius of 18 cm and a slant height of 30 cm?

How many liters of water can a hemispherical tank of radius 2.1 m contain? (Take \(\pi = \frac{22}{7}\)).

A solid metallic ball of radius 9 cm is melted and recast in to a right circular cylinder of double the radius of the ball. The curved surface area of the cylinder is :

The volume of a cylinder of height 32 cm and base diameter 36 cm is equal to the volume of a cone of height 24 cm. The curved surface area (in cm²) of the cone is:

The ratio of the heights of a right circular cone and a right circular cylinder is 8 : 9 and the ratio of the radii of their bases is 3 : 4. If the volume of the cylinder is 132 cm³, then the volume (in cm³) of the cone is:

The height and the radius of the base of a right circular cone are in the ratio of 12 : 5. If its volume is 314 cm³, then what is the slant height of the cone? (Use π = 3.14)

The difference between height and radius of the cylinder is 6 cm. The ratio of the radius and height of the cylinder is 4 : 5. Calculate the total surface area of the cylinder.

Find the cost of painting a ball that is in the shape of a sphere with a radius of 14 cm. The painting cost of the ball is ₹5 per square centimetre (take \(π = {22\over7}\)).

The radius of the right circular cylinder is thrice of its height. If the height of the cylinder is 2.1 cm, then what is the volume (approx.) of the cylinder.

What is the radius of a sphere having a volume of 4851cm³? (Use π = 22/7)

The capacity of a cylindrical tank is 38,500 litres. If the height is 4 metres, then what is the diameter of the base?

The surface area of a solid metallic sphere is 616 cm². It is melted and recast into a solid cone of height 28 cm. Find the diameter of the base of the cone so formed. (Take π = 22/7)

If the radius and height of a right circular cylinder are 21 cm and 5 cm, respectively, then the total surface area of cylinder is (use \(\pi =\frac{22}{7} \)):

Find the volume of a cone having base radius 3.5 cm and height 18 cm.

A sphere with an inner radius of 7 cm is fully filled with a chemical costing Rs.24 per cm³. What will be the cost of the chemical (in Rs.), if 50% is taken from the sphere?

What is the total surface area of a cone whose curved surface area is 550 cm² and radius is 7 cm? (Take \(\pi = {22\over7}\))

The curved surface area of a cylinder with a diameter of 20 cm is 1320 cm². What is the volume of the cylinder?

The circumference of the base of a cylindrical vessel is 44 cm, and its height is 25 cm. How many liters of water can it hold? (Take π = \(22\over 7\))

The volume of a right circular cylinder, if the radius of its base and the height are 7cm and 15cm, respectively, will be _______.

If the height and diameter of a cylinder are 12 cm and 28 cm, respectively, then find the ratio of the total surface area to the curved surface area.