Advertisements
Advertisements
प्रश्न
Rani bought a new field that is next to one she already owns in the given figure. This field is in the shape of a square of side 70 m. She makes a semi-circular lawn of maximum area in this field.
- Find the perimeter of the lawn.
- Find the area of the square field excluding the lawn.
उत्तर
i. Given, side of a square = 70 m
From the given figure, the diameter of semi-circle is same as the side of a square.
∴ Diameter of semi-circle = 70 m
∴ Diameter of semi-circle = Side of square
∴ Radius = `70/2` = 35 m .....`[∵ "Radius" = "Diameter"/2]`
∴ Perimeter of lawn = πr + 2r
= `22/7` × 35 + 2 × 35
= 110 + 70
= 180 m
ii. Area of square = Side × Side
= 70 × 70
= 4900 m2
∴ Required area = Area of square – Area of semi-circle
= `4900 - 1/2 xx π xx (35)^2` .....`[∵ "Area of semicircle" = 1/2 πr^2]`
= `4900 - 1/2 xx 22/7 xx 35 xx 35`
= 4900 – 1925
= 2975 m2
APPEARS IN
संबंधित प्रश्न
The length of the side of the square is given below. Find its area.
12 metre
The length of the side of the square is given below. Find its area.
18 cm
The length of the side of a square is given below. Find its area
16 cm
Trace your hand on the squared sheet on the page.
How will you decide whose hand is bigger-your hand or your friend’s hand?
What is the area of your hand? square cm.
What is the area of your friend’s hand? square cm.
The area of each square on a chess board is 4sqcm. Find the area of the board.
(a) At the beginning of game when all the chess men are put on the board, write area of the squares left unoccupied.
(b) Find the area of the squares occupied by chess men.
Here are some footprints of animals in actual sizes. Guess the area of their footprints.
Hen
Dog
A room is 4 m long and 3 m 50 cm wide. How many square metres of carpet are needed to cover the floor of the room?
Find the area of the shaded portion in a circle whose radius is 7 cm.
Study the layout given in the figure and answer the questions:
- Write an expression for the total area covered by both the bedrooms and the kitchen.
- Write an expression to calculate the perimeter of the living room.
- If the cost of carpeting is ₹ 50/m2, write an expression for calculating the total cost of carpeting both the bedrooms and the living room.
- If the cost of tiling is ₹ 30/m2, write an expression for calculating the total cost of floor tiles used for the bathroom and kitchen floors.
- If the floor area of each bedroom is 35 m2, then find x.
Calculate the area of shaded region in the given figure, where all of the short line segments are at right angles to each other and 1 cm long.
