Advertisements
Advertisements
Question
The largest possible sphere is carved out of a wooden solid cube of side 7 em. Find the volume of the wood left. (Use\[\pi = \frac{22}{7}\]).
Solution
Diameter of sphere curved out = side of cube = 7cm or Radius =3.5cm
Volume of cube = a3
=73
=343 cm3
Volume of sphere`=4/3pir^3`
`= 4/3 xx 22/7 xx 7/2 xx 7/2 xx 7/2 = 179.66 cm^3`
volume of the wood left=Volume of cube-volume of sphere
=343-179.66
=163.34 cm3
RELATED QUESTIONS
A solid wooden toy is in the form of a hemisphere surrounded 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 `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=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 wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in given figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.
[Use `pi = 22/7`]
The internal and external diameters of a hollow hemisphere vessel are 21cm and 25.2 cm The cost of painting 1cm2 of the surface is 10paise. Find total cost to paint the vessel all
over______?
Prove that the surface area of a sphere is equal to the curved surface area of the circumference cylinder__?
A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm, and height 3 cm. Find the area of its whole surface and volume.
Radii of circular ends of a solid frustum off a cone re 33cm and 27cm and its slant height are 10cm. find its total surface area?
A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 10459 `3/7` cm3. The radii of its lower and upper circular ends are 8cm and 20cm. find the cost of metal sheet used in making container at rate of Rs 1.4 per cm2?
A cylindrical bucket 28 cm in diameter and 72 cm high is full of water. The water is emptied into a rectangular tank 66 cm long and 28 cm wide. Find the height of the water level in the tank.
A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is `pir [sqrt(r^2 + h^2) + 3r + 2h]`.
