Gujarat Board Solutions Class 10 Maths Chapter 13 Surface Areas and Volumes Ex 13.3

Gujarat Board Solutions Class 10 Maths Chapter 13 Surface Areas and Volumes Ex 13.3

Gujarat Board Textbook Solutions Class 10 Maths Chapter 13 Surface Areas and Volumes Ex 13.3

Question 1.
A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
Solution:

Question 2.
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
Solution:
Radii of solid sphere are
r1 = 6 cm
r2 = 8 cm
and r3 = 10 cm
Let radius of resulting sphere be r.
Volume of three spheres = Volume of resulting sphere

Question 3.
A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform. [NCERT 20121]
Solution:

Question 4.
A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
Solution:
In case of cylindrical well
Diameter = 3 m

Question 5.
A container shaped like a right circular cylinder having a diameter 12 cm and a height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Solution:
In case of right circular cylinder, diameter = 12 cm
r1 = 6 cm
h1 = 15 cm
Volume of ice cream in right circular cylinder
= πr12h1
= π x 62 x 15
In case of cone
Diameter = 6 cm
Radius r2 = 3 cm
Height h2 = 12 cm

Question 6.
How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm x 10 cm x 3.5 cm?
Solution:

Question 7.
A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical help of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.
Solution:
In case of cylindrical bucket
Radius (r) of bucket = 18 cm
Height h = 32 cm
Volume of sand filled in cylindrical bucket
= πr2h
= π x 18x 32
= 10368 π cm3
In case of conical heap
Height (H) = 24 cm
Volume of conical heap = Volume of cylindrical bucket

Question 8.
Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?
Solution:
In case of canal
Width of canal (b) = 6 m
Depth of canal (h) = 1.5 m
Speed of flow of water = 10 km/h

Question 9.
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?
Solution:

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