Total surface area of a cone= .........

Frustum is a latin word, meaning ............

The slant height of the frustum of cone (l) = ................

Toy (Latto) is a solid which is a combination of ............. and .............

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 ..............

The shape of a gilli in the gilli danda game is a combination of ..............

Volume of the frustum of a cone is .............

The slant height of a bucket is 26 cm. The diameter of upper and lower circular ends are 36 cm and 16 cm. Find the height of the bucket.

Volume of the frustum of the cone is \(\frac { 1 }{ 3 } \pi \left( { R }^{ 2 }+{ r }^{ 2 }+Rr \right) \times h.\)

If we double the radius of a hemisphere, its urface area will also be doubled.

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

Conical flask is a combination of cylinder and the frustum of a cone.

A solid cylinder of radius 'r' and height 'h' is placed over other cylinder of same height and radius. The total surface area of the shape so formed is \(4\pi rh+2\pi { r }^{ 2 }\)

The dimensions of a metallic cuboid are 100cm x 80cm x 64cm.It is melted and recast into a cube.Find the surface area of the cube.

500 persons are taking a dip into a cuboidal pond which is 80 m long and 50 m broad. What is the rise of water level in the pond, if the average displacement of the water by a person is 0.04 m³ ?

Four cubes of volume 125 cm³ each are joined end to end, in a row. Find the surface area and volume of the resulting cuboid (see Fig.).

A milkman while supplying milk to their customer measures milk with a measuring cane which is cylindrical in shape with hemispherical raised bottom. The diameter of the measuring cylinder is 5 cm and height of the cylinder is 10 cm.
(i) Find the volume of measuring cane.
(ii) Which mathematical concept is used in given problem?
 

A rolling pin is made by joining three cylindrical pieces of wood as shown in the figure. Find the mass of the rolling pin with given measurements, if 1 cm³ of wood has approximately \(\frac { 1 }{ 2 } \)g mass. \(\left[ Use\ \pi =3.14 \right] \)

A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8 cm³ . The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of metal sheet used in making the bucket. \(\left[ Use\ \pi =3.14 \right] \)

A spherical shell of lead, whose external diameter is 18 cm, is melted and recast into a right circular cylinder, whose height is 8 cm and diameter 12 cm. Determine the internal diameter of the shell.

A godown building is in the form as shown in figure. The vertical cross-section parallel to the width side of the building is a rectangle of size 7 m x 3 m mounted by a semicircle of radius 3.5 m. The inner measurements of the cuboid are 10 m x 7 m x 3 m. Find the total internal surface area excluding the floor.

A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm, Find. the height of the each bottle, if 10% liquid is wasted in this transfer.

Water is flowing at the rate of 2.52 km/h through a cylindrical pipe into a cylindrical tank, the radius of whose base is 40 cm, if the Increase in the level of water in the tank, in half an hour is 3.15 m, find the internal diameter of the pipe.

Ashwani, a factory owner wants to thank all his workers by gifting a decorated spherical ball. The diameter of the sphere is (2a+5) cm. Each ball is to be packed in a right circular cylindrical box which just encloses a sphere as shown in the figure.
If the height of the cylinder is 21 cm, then 
(i) what is the value of a?
(ii) what is the curved surface area of a sphere?
(iii) which value are shown by Ashwani?

150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.