RS Aggarwal Solutions Chapter 13 Volume and Surface Area Ex 13D in PDF for Free Download
Find the volume and surface area of a sphere whose radius is :
(i) 3.5 cm (ii) 4.2 cm (iii) 5m
(i) Radius of sphere = 3.5cm
(a) Volume = πr3
The volume of a sphere is 38808 cm3 . Find its radius and hence surface area
Let r be the radius of the sphere and volume = 38808 cm3
∴ πr3 = 38803
=> x r3 = 38803
Find the surface area of a sphere whose volume is 606.375 m3.
Let r be the radius of the sphere
∴ Volume = πr3
The surface area of a sphere is 394.24 m2. Find its radius and volume.
Surface area of a sphere = 394.24 m2
Let r be the radius, then 4πr2 = 394.24
The surface area of a sphere is (576π) cm2. Find its volume.
Surface area of sphere = 576π cm2
Let r be the radius, then 4r2 = 576π
The outer diameter of a spherical shell is 12cm and its inner diameter is 8cm. Find the volume of metal contained in the shell. Also, find its outer Surface area.
Outer diameter of shell = 12cm,
Outer radius (R) = = 6cm
and inner diameter = 8cm
How many lead shots, each 3mm in diameter, can be made from a cuboid with dimensions (12cm x 11cm x 9cm)
Length of cuboid of (l) = 12cm
Breadth (b) = 11cm
and height (h) = 9cm
How many lead balls, each of radius 1cm, can be made from a sphere of radius 8cm ?
Radius of sphere (r) = 8cm
Volume = πr3
A solid sphere of radius 3cm is melted and then cast into smaller spherical balls, each of diameter 0.6cm. Find the number of small balls thus obtained.
Radius of solid sphere (R) = 3cm.
Volume = π(R)3 = π(3)3 cm3
A metallic sphere of radius 10.5 cm is melted and then recast into smaller cones, each of radius 3.5cm and height 3cm. How many cones are obtained ?
Radius of metallic sphere (R) = 10.5cm
How many spheres 12cm in diameter can be made from a metallic cylinder of diameter 8cm and height 90cm ?
Diameter of a cylinder = 8cm
Radius (r) = = 4cm
The diameter of a sphere is 6cm. It is melted and drawn into a wire of diameter 2mm. Find the length of the wire.
Diameter of sphere = 6cm
Radius (R) = = 3cm
The diameter of a copper sphere is 18cm. It is melted and drawn into a long wire of uniform cross section. If the length qf the wire is 108m, find its diameter.
Diameter of sphere = 18cm
Radius (R) = = 9cm.
A sphere of diameter 15.6cm is melted and cast into a right circular cone of height 31.2 cm. Find the diameter of the base of the cone.
Diameter of the sphere = 15.6 cm
Radius (R) = = 7.8 cm
A spherical canonball 28cm in diameter is melted and cast into a right circular cone mould, whose base is 35 cm in diameter. Find the height of the cone.
Diameter of the canonball = 28cm
Radius (R) = = 14 cm
A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball.
Radius of spherical big ball (R) = 3cm
The radii of two spheres are in the ratio 1 : 2. Find the ratio of their surfaces areas.
Ratio in the radii of two spheres = 1:2
Let radius of smaller sphere = r then,
radius of bigger sphere = 2r
The surface areas of two spheres are in the ratio 1 : 4. Find the ratio of their volumes.
Let r1 and r2 be the radii of two spheres
A cylindrical tub of radius 12 cm contains water to a depth of 20cm. A spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball ?
Radius of the cylindrical tub = 12cm.
First level of water = 20cm
Raised water level = 6.75cm.
A cylindrical bucket with base radius 15cm is filled with water up to a height of 20cm. A heavy iron spherical ball of radius9 cm is dropped into the bucket to submerge completely in the water. Find the increase in the level of water.
Radius of the ball (r) = 9cm.
Volume of ball = πr³
A hemisphere of lead of radius 9cm is cast into a right circular cone of height 72cm. Find the radius of the base of the cone.
Radius of hemisphere of lead (r) = 9cm.
A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 4 cm . How many bottles are required to empty the bowl?
Radius of hemispherical bowl (r) = 9cm
A hollow spherical shell is made of a metal of density 4.5 g per cm³. If its internal and external radii are 8cm and 9cm respectively, find the weight of the shell.
External radius of spherical shell (R) = 9cm
A hemispherical bowl is made of steel 0.5cm thick. The inside radius of the bowl is 4cm. Find the volume of steel used in making the bowl.
Inner radius (r) = 4 cm
Thickness of steel used = 0.5