Q.1 The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.
Solution : Diameter of the sphere = 7 m. Therefore, radius is 3.5 m. So, the riding
space available for the motorcyclist is the surface area of the ‘sphere’ which is
given by
4pr2 = 4 ×22 / 7× 3.5 × 3.5 m2
= 154 m2
Q.2 A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6 m, find the cost of painting it, given the cost of painting is ` 5 per 100 cm2.
Solution : Since only the rounded surface of the dome is to be painted, we would need to find the curved surface area of the hemisphere to know the extent of painting that needs to be done. Now, circumference of the dome = 17.6 m. Therefore, 17.6 = 2pr.
So, the radius of the dome = 17.6 ×
7/ 2 ??22 m = 2.8 m
The curved surface area of the dome = 2?r2
= 2 × 22/ 7 × 2.8 × 2.8 m2
= 49.28 m2
Now, cost of painting 100 cm2 is ` 5.
So, cost of painting 1 m2 = ` 500
Therefore, cost of painting the whole dome
= ` 500 × 49.28
= ` 24640
Q.3 A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm × 12 cm × 8 cm, how many bricks would be
required?
Solution : Since the wall with all its bricks makes up the space occupied by it, we
need to find the volume of the wall, which is nothing but a cuboid.
Here, Length = 10 m = 1000 cm
Thickness = 24 cm
Height = 4 m = 400 cm
Therefore, Volume of the wall = length × thickness × height
= 1000 × 24 × 400 cm3
Now, each brick is a cuboid with length = 24 cm, breadth = 12 cm and height = 8 cm
So, volume of each brick = length × breadth × height
= 24 × 12 × 8 cm3
So, number of bricks required =
volume of the wall
volume of each brick
=
1000 × 24 × 400
24× 12 × 8
= 4166.6
So, the wall requires 4167 bricks
Q.4 A child playing with building blocks, which are of the shape of cubes, has built a structure. If the edge of each cube is 3 cm, find the volume of the structure built by the child.
Solution : Volume of each cube = edge × edge × edge
= 3 × 3 × 3 cm3 = 27 cm3
Number of cubes in the structure = 15
Therefore, volume of the structure = 27 × 15 cm3
= 405 cm3
Q.5 The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10 m, how much concrete mixture would be required to build 14 such pillars?
Solution : Since the concrete mixture that is to be
used to build up the pillars is going to occupy the
entire space of the pillar, what we need to find here
is the volume of the cylinders.
Radius of base of a cylinder = 20 cm
Height of the cylindrical pillar = 10 m = 1000 cm
So, volume of each cylinder = ?r2h
=
22/7 * 20* 20 *1000?cm3
=
8800000/7 cm3
=
8.8 / 7 m3 (Since 1000000 cm3 = 1m3)
Therefore, volume of 14 pillars = volume of each cylinder × 14
=
8.8/7 * 14
= 17.6 m3
So, 14 pillars would need 17.6 m3 of concrete mixture.
