Maths-
General
Easy
Question
A Rectangular room is 18 m long and 12 m wide. A path 2 m wide is all around it. Find the cost of constructing the path at the rate of Rs 100 per sq. metre.
Hint:
Area of a rectangle = Length × breadth
The correct answer is: ∴ Cost of constructing the path is Rs. 13,600.
Step-by-step solution:-
From the adjacent diagram,
Let the outer rectangle represent the path around the room.
∴ Length of the outer rectangle = length of the room + 2 (width of the path)
∴ Length of the outer rectangle = 18 + 2 (2)
∴ Length of the outer rectangle = 18 + 4
∴ Length of the outer rectangle = 22 m ........................................................... (Equation i)
Also, breadth of the outer rectangle = breadth of the field + 2 (width of the path)
∴ breadth of the outer rectangle = 12 + 2 (2)
∴ breadth of the outer rectangle = 12 + 4
∴ breadth of the outer rectangle = 16 m .................................................. (Equation ii)
We need to find the cost of contructing the path, i.e. the entire surface area of the path i.e. Area of the path
Area of the outer rectangle = length × breadth
∴ Area of the outer rectangle = 22 × 16 ......................................................... (From Equations i & ii)
∴ Area of the outer rectangle = 352 m2 ............................................................ (Equation iii)
Area of the room = length × breadth
∴ Area of the room = 18 × 12 ......................................................................... (From given information)
∴ Area of the room = 216 m2 .......................................................................... (Equation iv)
Now, Area of the path = Area of outer rectangle - Area of the inner room
∴ Area of the path = 352 - 216 ............................................................ (From Equations iii & iv)
∴ Area of the path = 136 m2 .................................................................... (Equation v)
Now, cost of constructing the path @ Rs. 100 per sq. mt. = Area of the path × rate of constructing 1 sq mt
∴ cost of constructing the path @ Rs. 100 per sq. mt. = 136 × 100 .................... (From given information & Equation v)
∴ cost of constructing the path @ Rs. 100 per sq. mt. = Rs. 13,600
Final Answer:-
∴ Cost of constructing the path is Rs. 13,600.
Related Questions to study
Maths-
Identify the correct congruence statement.
Identify the correct congruence statement.
Maths-General
Maths-
Prove that the given triangles are congruent and write the congruence statement.
Prove that the given triangles are congruent and write the congruence statement.
Maths-General
Maths-
A square shaped playground is divided into two parts by putting
a boundary across a diagonal as shown in the diagram. Are the two parts Congruent?
A square shaped playground is divided into two parts by putting
a boundary across a diagonal as shown in the diagram. Are the two parts Congruent?
Maths-General
Maths-
In △ ABC , AB = 3. BC = 4, AC = 5 .Check whether the coordinates (2,3), (5,7) and (5, 3) form the vertices of a triangle congruent to △ABC
In △ ABC , AB = 3. BC = 4, AC = 5 .Check whether the coordinates (2,3), (5,7) and (5, 3) form the vertices of a triangle congruent to △ABC
Maths-General
Maths-
Which of the following congruence statements is true?
Which of the following congruence statements is true?
Maths-General
Maths-
Use the SSS congruence postulate and prove that the given triangles are congruent
Use the SSS congruence postulate and prove that the given triangles are congruent
Maths-General
Maths-
Use the SSS congruence postulate and prove that the given triangles are congruent.
Use the SSS congruence postulate and prove that the given triangles are congruent.
Maths-General
Maths-
Mark has two triangular shaped fields as shown below. Are two fields congruent? Explain why or why not.
Mark has two triangular shaped fields as shown below. Are two fields congruent? Explain why or why not.
Maths-General
Maths-
A Toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other end. The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radii of hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy if the height of the conical part is 12 cm
A Toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other end. The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radii of hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy if the height of the conical part is 12 cm
Maths-General
Maths-
A Sphere, cylinder and a cone are of the same radius and same height . Find the ratio of their curved surface areas and their volumes?
A Sphere, cylinder and a cone are of the same radius and same height . Find the ratio of their curved surface areas and their volumes?
Maths-General
Maths-
From a solid wooden cylinder of 25 cm height and 6 cm diameter , two conical cavities are hollowed out , The diameters of the cones are also of 6 cm and the height is 10.5 cm, Find the volume of the remaining solid ?
From a solid wooden cylinder of 25 cm height and 6 cm diameter , two conical cavities are hollowed out , The diameters of the cones are also of 6 cm and the height is 10.5 cm, Find the volume of the remaining solid ?
Maths-General
Maths-
From a solid circular cylinder of 5 cm radius and 12 cm height , a conical cavity of the same base radius and of the same height is hollowed out. Find the volume of the remaining solid ?
From a solid circular cylinder of 5 cm radius and 12 cm height , a conical cavity of the same base radius and of the same height is hollowed out. Find the volume of the remaining solid ?
Maths-General
Maths-
A hemispherical container of 4 cm radius is filled to the brim with milk . The milk is then poured in a vertical right circular cone of 8 cm radius and 16 cm height. What percentage of the vertical right circular cone remains empty ?
A hemispherical container of 4 cm radius is filled to the brim with milk . The milk is then poured in a vertical right circular cone of 8 cm radius and 16 cm height. What percentage of the vertical right circular cone remains empty ?
Maths-General
Maths-
An ice cream cone is in the union of a right circular cone and hemisphere that has the same base as the cone . Find the Volume of the ice cream if the height of the cone is 9 cm and radius of its base is 2.5 cm.
An ice cream cone is in the union of a right circular cone and hemisphere that has the same base as the cone . Find the Volume of the ice cream if the height of the cone is 9 cm and radius of its base is 2.5 cm.
Maths-General
Maths-
A Hemispherical bowl of 36 cm internal diameter contains a liquid. This liquid is to be filled into right circular cone shaped bottles of 3 cm radius and 18 cm height , How many bottles are required to empty the bowl ?
A Hemispherical bowl of 36 cm internal diameter contains a liquid. This liquid is to be filled into right circular cone shaped bottles of 3 cm radius and 18 cm height , How many bottles are required to empty the bowl ?
Maths-General
