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
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
APPEARS IN
RELATED QUESTIONS
Find the surface area of a sphere of radius 10.5 cm.
`["Assume "pi=22/7]`
Find the surface area of a sphere of diameter 3.5 m.
`["Assume "pi=22/7]`
Find the total surface area of a hemisphere of radius 10 cm. [Use π = 3.14]
Find the radius of a sphere whose surface area is 154 cm2.
`["Assume "pi=22/7]`
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 solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.
Find the surface area of a sphere of radius 10.5 cm .
A spherical ball of lead has been melted and made into identical smaller balls with radius equal to half the radius of the original one. How many such balls can be made?
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 radius of the solid sphere.
- the number of cones recast. [Take π = 3.14]
How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?
The total surface area of a hemisphere of radius r is
A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is
The radius of a sphere is 9 cm. It is melted and drawn into a wire of diameter 2 mm. Find the length of the wire in metre.
The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate : the number of cones recast. `("Take" pi =22/7)`
A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones used.
A conical tent is to accommodate 77 persons. Each person must have 16 m3 of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area.
The volume of a sphere is 905 1/7 cm3, find its diameter.
There is surface area and volume of a sphere equal, find the radius of sphere.
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is ______.
