There are two figures, a triangle with sides 3cm, 5cm , 2cm and a rectangle whose
length is 6cm and breadth is 4cm. Which of the two figures have larger
boundary?
Answers
Question 14:
A circular flower garden has an area of 314 m2. A sprinkler at the centre of the garden can cover an area that has a radius of 12 m. Will the sprinkler water the entire garden? (Take π = 3.14)
ANSWER:
Area = πr2 = 314 m2
3.14 × r2 = 314
r2 = 100
r = 10 m
Question 15:
Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take π = 3.14)
ANSWER:
Radius of outer circle = 19 m
Circumference = 2πr = 2 × 3.14 × 19 = 119.32 m
Radius of inner circle = 19 − 10 = 9 m
Circumference = 2πr = 2 × 3.14 × 9 = 56.52 m
Question 16:
How many times a wheel of radius 28 cm must rotate to go 352 m?
(Take π )
ANSWER:
r = 28 cm
Circumference = 2πr = = 176 cm
Number of rotations =
Therefore, it will rotate 200 times.
Question 17:
The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour. (Take π = 3.14)
ANSWER:
Distance travelled by the tip of minute hand = Circumference of the clock
= 2πr = 2 × 3.14 × 15
= 94.2 cm
Question 1:
A garden is 90 m long and 75 m broad. A path 5 m wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectare.
ANSWER:
Length (l) of garden = 90 m
Breadth (b) of garden = 75 m
Area of garden = l × b = 90 × 75 = 6750 m2
From the figure, it can be observed that the new length and breadth of the garden, when path is also included, are 100m and 85m respectively.
Area of the garden including the path = 100 × 85 = 8500 m2
Area of path = Area of the garden including the path − Area of garden
= 8500 − 6750 = 1750 m2
1 hectare = 10000 m2
Therefore, area of garden in hectare
Question 2:
A 3 m wide path runs outside and around a rectangular park of length 125 m and breadth 65 m. Find the area of the path.
ANSWER:
Length (l) of park = 125 m
Breadth (b) of park = 65 m
Area of park = l × b = 125 × 65 = 8125 m2
From the figure, it can be observed that the new length and breadth of the park, when path is also included, are 131 m and 71 m respectively.
Area of the park including the path = 131 × 71 = 9301 m2
Area of path = Area of the park including the path − Area of park
= 9301 − 8125 = 1176 m2
Question 3:
A picture is painted on a cardboard 8 cm long and 5 cm wide such that there is a margin of 1.5 cm along each of its sides. Find the total area of the margin.
ANSWER:
Length (l) of cardboard = 8 cm
Breadth (b) of cardboard = 5 cm
Area of cardboard including margin = l × b = 8 × 5 = 40 cm2
From the figure, it can be observed that the new length and breadth of the cardboard, when margin is not included, are 5 cm and 2 cm respectively.
Area of the cardboard not including the margin = 5 × 2 = 10 cm2
Area of the margin = Area of cardboard including the margin − Area of cardboard not
= 40 − 10 = 30 cm2
Question 4:
A verandahof width 2.25 m is constructed all along outside a room which is 5.5 m long and 4 m wide. Find:
(i) the area of the verandah
(ii) the cost of cementing the floor of the verandah at the
Question 7:
Through a rectangular field of length 90 m and breadth 60 m, two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the fields. If the width of each road is 3 m, find
(i) the area covered by the roads.
(ii)the cost of constructing the roads at the rate of Rs 110 per m2.
ANSWER:
Length (l) of field = 90 m
Breadth (b) of field = 60 m
Area of field = 90 × 60 = 5400 m2
Length of road PQRS = 90 m
Length of road ABCD = 60 m
Width of each road = 3 m
Area of the roads = ar (PQRS) + ar (ABCD) − ar (KLMN)
= (90 × 3) + (60 × 3) − (3 × 3)
= 270 + 180 − 9 = 441 m2
Cost for constructing 1 m2 road = Rs 110
Cost for constructing 441 m2 road = 110 × 441 = Rs 48510
Step-by-step explanation:
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