Volume of a spherical shell = ...........

If the surface area of a sphere is 6161 cm², then its radius is equal to ...............

If the ratio between the volume of two spheres is 27 : 8, then ratio between their surface areas is ..............

All faces of a cuboid must be rectangular.

Two cubes each of edge 10 cm, are joined end to end. The surface area of the resulting cuboid is 900 cm².

The curved surface area of the frustum of the cone is given by \(S=\pi \left( { r }_{ 1 }+{ r }_{ 2 } \right) l\)

A conical military tent having diameter of the base 24m and slant height of the tent is 13m, find the curved surface area cone.\([\pi={22\over7}]\)

Find the radius of a sphere whose surface area is 154cm²

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

If a right circular cylinder just encloses a sphere of radius r.Find curved surface area of the cylinder.

A gulab jamun, contains sugar syrup up to about 30% of its volume.Find approximately how much syrup would be found  in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5cm and diameter 2.8cm . (see figure).

The sum of the radius of the base and the height of a solid cylinder is 37cm.If the total surface area of the of the solid cylinder is 1628cm², find the volume of the cylinder.\([\pi=22/7]\)

A heap of wheat is in the form of a cone of diameter 9m and height 3.5m.Find its volume.How much canvas cloth is required to just cover the heap? (Use \(\pi=3.14\))

A hemisphere bowl of internal radius 9cm is full of water.Its contents are emptied in a cylindrical vessel of internal radius 6cm.Find the height of water in the cylindrical vessel.

A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166\(\frac{5}{6}\) cm³. Find the height of the toy. also, find the cost of painting the hemispherical part of the toy at the rate of Rs.10 per cm².[Use \(\pi=\frac{22}{7}\)]

The lower portion of a haystack is an inverted cone frustum and upper part is a cone. Find the lateral surface area of the haystack. \(\left[ Use\quad \pi =3.14 \right] \) 

A storage oil tanker consists of a cylindrical portion 7 m in diameter with two hemispherical ends of the same diameter. The oil tanker lying horizontally. If the total length of the tanker is 20 m, then find the capacity of the container.

A tent is in the shape of a right circular cylinder up to a height of 3m and then becomes a right circular cone with a maximum height of 13.5m above the ground.Calculate the cost of painting the inner side of the tent at the rate of Rs.2 per m² , if the radius of the base is 14m.

Water flows out through a circular pipe whose internal radius is 1 cm, at the rate of 80 cm/second into an empty cylindrical tank, the radius of whose base is 40 cm. By how much will the level of water rise in the tank in half an hour?

A bucket of height 16 cm is made up of metal sheet in the form of frustum of a right circular cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the volume of milk which can be filled in the bucket. Also find the cost of making the bucket when the metal sheet costs Rs. 15 per 100 cm² .

A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 10459\(\frac{3}{7}\)cm³. The radii of its lower and upper circular ends are 8 cm and 20 cm respectively. Find the cost of metal sheet used in making the container at the rate of Rs.1.40 per square centimetre. [Use \(\pi=\frac{22}{7}\)]