Advertisements
Advertisements
प्रश्न
The largest cone is curved out from one face of solid cube of side 21 cm. Find the volume of the remaining solid.
Advertisements
उत्तर
The radius of the largest possible cone is carved out of a solid cube is equal to the half of the side of the cube.
Also, the height of the cone is equal to the side of the cube.
Radius of the cone = \[\frac{21}{2} = 10 . 5\]
Volume of the remaining solid = Volume of cube − Volume of cone
\[= \left( \text { Side } \right)^3 - \frac{1}{3}\pi r^2 h\]
\[ = \left( 21 \right)^3 - \frac{1}{3} \times \frac{22}{7} \times \left( 10 . 5 \right)^2 \times 21\]
\[ = 9261 - 2425 . 5\]
\[ = 6835 . 5 {cm}^3\]
Disclaimer: The answer given in the book is not correct.
APPEARS IN
संबंधित प्रश्न
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 each bottle, if 10% liquid is wasted in this transfer.
Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/h. How much area will it irrigate in 10 minutes, if 8 cm of standing water is needed for irrigation?
In Fig. 5, is a decorative block, made up two solids – a cube and a hemisphere. The base of the block is a cube of side 6 cm and the hemisphere fixed on the top has diameter of 3.5 cm. Find the total surface area of the bock `(Use pi=22/7)`
A medicine capsule is in the shape of cylinder with two hemispheres stuck to each of its ends (see the given figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area. [Use π = `22/7`]
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2
[use `pi = 22/7`]
A bucket has top and bottom diameter of 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm2 . (Use π = 3.14)
If the radii of circular ends of a bucket 24cm high are 5cm and 15cm. find surface area of
bucket?
If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:
A solid cuboid of iron with dimensions 53 cm ⨯ 40 cm ⨯ 15 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe.
A solid is in the form of a cylinder with hemispherical ends. Total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the volume and total surface area of the solid.
Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?
If the total surface area of a solid hemisphere is 462 cm2, then find its volume.
A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm, respectively. The radii of the hemispherical and the conical parts are the same as that of the cylindrical part. Find the surface area of the toy, if the total height of the toy is 30 cm.
In a right circular cone, the cross-section made by a plane parallel to the base is a
A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere and hence find the surface area of this sphere.
In the figure given below, ABCD is a square of side 14 cm with E, F, G and H as the mid points of sides AB, BC, CD and DA respectively. The area of the shaded portion is ______.
If the volumes of a cube is 1728 cm³, the length of its edge is equal to ______.
The shape of a gilli, in the gilli-danda game (see figure), is a combination of ______.
Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.
The total surface area of a solid hemisphere of radius 7 cm is ______.
