Advertisements
Advertisements
Question
From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find: the volume of remaining solid
Advertisements
Solution
Dimensions of rectangular solids = `=(42xx30xx20) "cm"`
volume=`(42xx30xx20)=25200 "cm"^3 `
Radius of conical cavity (r) =7 cm
height (h)=24 cm
Volume of cone=`1/3pir^2h`
=`1/3xx22/7xx7xx7xx24`
`= 1232 "cm"^3`
Volume of remaining solid =` (25200-1232)=23968 "cm"^3`
Radius of conical cavity (r) =7 cm
height (h) = 24 cm
Volume of cone = `1/3 pi "r"^2"h"`
`= 1/3 xx 22/7 xx 7 xx 7 xx 24`
= 1232 cm3
Volume of remaining solid = (25200 - 1232) = 23968 cm3
RELATED QUESTIONS
On a map drawn to a scale of 1: 50,000, a rectangular plot of land ABCD has the following dimensions. AB = 6 cm; BC = 8 cm and all angles are right angles. Find:
1) the actual length of the diagonal distance AC of the plot in km.
2) the actual area of the plot in sq. km.
A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved
surface area of the shape if the length of the shape be 7 cm.
The volume of a sphere is 38808 cm3; find its diameter and the surface area.
A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.
A sphere has the same curved surface area as the curved surface area of a cone of height 36 cm and base radius 15 cm . Find the radius of the sphere .
The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find volume of material of the vessel.
The total area of a solid metallic sphere is 1256 cm2. It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate: the number of cones recasted [π = 3.14]
The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into smaller spheres of diameter 3.5 cm. How many such spheres can be obtained?
A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of the balls are 1.5 cm and 2 cm. Find the diameter of the third ball.
A solid sphere is cut into two identical hemispheres.
Statement 1: The total volume of two hemispheres is equal to the volume of the original sphere.
Statement 2: The total surface area of two hemispheres together is equal to the surface area of the original sphere.
Which of the following is valid?
