Advertisements
Advertisements
प्रश्न
A spherical glass vessel has a cylindrical neck 8 cm long, 2cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 cm3. Check whether she is correct, taking the above as the inside measurements, and π = 3.14
उत्तर
Height (h) of cylindrical part = 8 cm
Radius (r2) of cylindrical part = `2/2` = 1 cm
Radius (r1) spherical part = `8.5/2` = 4.25 cm
Volume of vessel = Volume of sphere + Volume of cylinder
= `4/3pir_1^3+pir_2^2h`
= `4/3pi(8.5/2)^3 +pi(1)^2(8)`
= `4/3xx3.14xx76.765625 + 8 xx 3.14`
= 321.392 + 25.12
= 3346.512
= 346.51 cm3
Hence, she is wrong.
APPEARS IN
संबंधित प्रश्न
What length of a solid cylinder 2cm in diameter must be taken to recast into a hollow
cylinder of length 16cm, external diameter 20cm and thickness 2.5mm?
A hollow sphere of internal and external radii 2cm and 4cm is melted into a cone of basse radius 4cm. find the height and slant height of the cone______?
A solid piece of iron of dimensions 49 × 33 × 24 cm is moulded into a sphere. The radius of the sphere is
A solid metallic sphere of radius 8 cm is melted and recast into spherical balls each of radius 2 cm. Find the number of spherical balls obtained.
A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75 cm. Find the radius of the base of the cone.
A hollow sphere of external and internal diameters 8 cm and 4 cm, respectively is melted into a solid cone of base diameter 8 cm. Find the height of the cone.
Rainfall in an area is 5 cm. The volume of the water that falls on 2 hectares of land is
A hemispherical bowl of internal diameter 30 cm is full of a liquid. This liquid is poured into cylindrical bottles of diameter 5 cm and height 6 cm each. How many bottles are required?
The given figure shows a solid formed of a solid cube of side 40 cm and a solid cylinder of radius 20 cm and height 50 cm attached to the cube as shown.
Find the volume and the total surface area of the whole solid. [Take π = 3.14].
Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/hour. How much area will it irrigate in 30 minutes; if 8 cm standing water is needed?
In the given figure, AB is the diameter of a circle with center O and OA = 7 cm. Find the area of the shaded region.
The radius of a wire is decreased to one third. If volume remains the same, the length will become ______.
A solid piece of iron in the form of a cuboid of dimensions 49 cm × 33 cm × 24 cm, is moulded to form a solid sphere. The radius of the sphere is ______.
A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of entire capsule is 2 cm. The capacity of the capsule is ______.
A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is `4/3 pia^3`.
How many shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9 cm × 11cm × 12cm?
Two solid cones A and B are placed in a cylinderical tube as shown in the figure. The ratio of their capacities are 2:1. Find the heights and capacities of cones. Also, find the volume of the remaining portion of the cylinder
A solid iron cuboidal block of dimensions 4.4 m × 2.6 m × 1 m is recast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.
The rain water from a roof of dimensions 22 m × 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall in cm.
The sum of the length, breadth and height of a cuboid is `6sqrt(3)` cm and the length of its diagonal is `2sqrt(3)` cm. The total surface area of the cuboid is ______.
