ICSE

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.1

Question 1.
The length and breadth of a rectangular field are in the ratio 9 : 5. If the area of the field is 14580 square metres, find the cost of surrounding the field with a fence at the rate of ₹3·25 per metre.
Solution:

Question 2.
A rectangle is 16 m by 9 m. Find a side of the square whose area equals the area of the rectangle. By how much does the perimeter of the rectangle exceed the perimeter of the square?
Solution:

Question 3.
Two adjacent sides of a parallelogram are 24 cm and 18 cm. If the distance between longer sides is 12 cm, find the distance between shorter sides.
Solution:

Question 4.
Rajesh has a square plot with the measurement as shown in the given figure. He wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of ₹50 per m².

Solution:

Question 5.
A flooring tile has a shape of a parallelogram whose base is 18 cm and the corresponding height is 6 cm. How many such tiles are required to cover a floor of area 540 m²? (If required you can split the tiles in whatever way you want to fill up the comers).
Solution:

Question 6.
An ant is moving around a few food pieces of different shapes scattered on the floor. For which food piece would the ant have to take a longer round?

Solution:

Question 7.
In the adjoining figure, the area enclosed between the concentric circles is 770 cm2. If the radius of the outer circle is 21 cm, calculate the radius of the inner circle.

Solution:

Question 8.
A copper wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent into the form of a circle, find the area of the circle.
Solution:

Question 9.
From the given figure, find
(i) the area of ∆ ABC
(ii) length of BC
(iii) the length of altitude from A to BC

Solution:

Question 10.
A rectangular garden 80 m by 40 m is divided into four equal parts by two cross-paths 2.5 m wide. Find
(i) the area of the cross-paths.
(ii) the area of the unshaded portion.

Solution:

Question 11.
In the given figure, ABCD is a rectangle. Find the area of the shaded region.

Solution:

Question 12.
In the adjoining figure, ABCD is a square grassy lawn of area 729 m². A path of uniform width runs all around it. If the area of the path is 295 m², find
(i) the length of the boundary of the square field enclosing the lawn and the path.
(ii) the width of the path.

Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 17 Visualising Solid Shapes Check Your Progress

Question 1.
Write the number of faces, vertices and edges of a
(i) hexagonal pyramid
(ii) octagonal pyramid
(iii) decagonal pyramid
(iv) nonagonal pyramid
(v) heptagonal prism
(vi) decagonal prism.
Solution:

Question 2.
Give three examples of 3-dimensional shapes around you which are the combinations of 2 or more 3-dimensional shapes.
Solution:

Question 3.
Give two examples of solids which are not polyhedrons.
Solution:

Question 4.
Why a pentagonal pyramid having all its edges congruent cannot be a regular polyhedron?
Solution:

Question 5.
In a polyhedron, if F = 8 and V = 12 then find the number of edges.
Solution:

Question 6.
Verify Euler’s formula for the following figures:

Solution:

Question 7.
For each of the given solid, the three views are given. Identify for each solid the corresponding top, front and side views:


Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 17 Visualising Solid Shapes Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) A solid made up of polygonal regions is called ………
(ii) Polyhedrons which are not convex are called ………
(iii) A polyhedron is said to be ……… if all of its faces are regular polygons and the same number of faces meet at each vertex.
(iv) A polyhedron whose base and top are congruent polygons and whose lateral faces are parallelograms in shape is called a ………
(v) A prism whose base and top are congruent hexagon is called a ………
(vi) A polyhedron whose all lateral faces are triangles is called a ………
(vii) A triangular pyramid is also known as ………
(viii) A rectangular prism is also known as ………
(ix) The polygonal regions forming a polyhedron are called ………
Solution:

Question 2.
State which of the following statements are true (T) or false (F):
(i) A cylinder is a polyhedron.
(ii) All the prisms and pyramids are polyhedrons.
(iii) A tetrahedron is the only pyramid which can be a regular polyhedron.
(iv) The line segments where the faces of a polyhedron meet are called edges.
(v) F + E = V + 2 is called a Euler’s formula.
(vi) In any prism number of faces is 2 more than number of sides of polygonal base.
(vii) In any pyramid number of edges is twice the number of sides of polygonal base.
(viii) An octagonal prism has 18 vertices.
(ix) All pyramids are prisms.
(x) Lateral faces of a pyramid are triangles.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 17):
Question 3.
Which of the following is not a 2-dimensional shape?
(a) Triangle
(b) Circle
(c) Sphere
(d) Rectangle
Solution:

Question 4.
Which of the following is a 3-dimensional shape?
(a) Parallelogram
(b) Cylinder
(c) Square
(d) none of these
Solution:

Question 5.
Name the pyramid shown in the given figure.

(a) Nonagonal pyramid
(b) Octagonal pyramid
(c) Decagonal pyramid
(d) Hexagonal pyramid
Solution:

Question 6.
How many parallel and congruent faces does a cylinder have?
(a) 4
(b) 3
(c) 2
(d) none
Solution:

Question 7.
How many pairs of congruent parallel faces does a rectangular prism have?
(a) 8
(b) 6
(c) 4
(d) 3
Solution:

Question 8.
How many congruent isosceles triangles does a square pyramid have?
(a) 2
(b) 4
(c) 6
(d) 8
Solution:

Question 9.
Which amongst the following is not a polyhedron?

Solution:

Question 10.
Which of the following is not a prism?

Solution:

Question 11.
The number of triangular faces of a triangular prism is
(a) 2
(b) 3
(c) 4
(d) 5
Solution:

Question 12.
The number of edges in a pentagonal pyramid is
(a) 5
(b) 10
(c) 15
(d) 20
Solution:

Question 13.
The number of rectangular faces in a hexagonal prism is
(a) 6
(b) 8
(c) 10
(d) 12
Solution:

Question 14.
In a polyhedron E = 15, V = 10, then F is
(a) 3
(b) 5
(c) 7
(d) 9
Solution:

Question 15.
In a polyhedron F = 5, E = 8, then V is
(a) 3
(b) 5
(c) 7
(d) 9
Solution:

Question 16.
In a polyhedron F = 17, V = 30, then E is
(a) 30
(b) 45
(c) 60
(d) none of these
Solution:

Question 17.
A polyhedron has 4 faces, 4 vertices and 6 edges. Name the polyhedron.
(a) A rectangular prism
(b) A triangular prism
(c) A rectangular pyramid
(d) A triangular pyramid
Solution:

Higher Order Thinking Skills (Hots)
Question 1.
Which of the following nets can be folded to form a cone?

Solution:

Question 2.
Which of the following nets can be folded to form a cylinder?

Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 17 Visualising Solid Shapes Ex 17.2

Question 1.
Can a polyhedron have for its faces
(i) 3 triangles?
(ii) 4 triangles?
(iii) a square and four triangles?
Solution:

Question 2.
Which are prisms among the following?

Solution:

Question 3.
Verify Euler’s formula for these solids:

Solution:

Question 4.
Can a polyhedron have 15 faces, 30 edges and 20 vertices?
Solution:

Question 5.
If a polyhedron has 8 faces and 8 vertices, find the number of edges.
Solution:

Question 6.
If a polyhedron has 7 faces and 10 vertices, find the number of edges.
Solution:

Question 7.
Write the number of faces, vertices and edges in
(i) an octagonal prism
(ii) decagonal pyramid.
Solution:

Question 8.
Using Euler’s formula, complete the following table:

Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 17 Visualising Solid Shapes Ex 17.1

Question 1.
Match the objects with their shapes:


Solution:

Question 2.
For each of the given solid, the two views are given. Match for each solid the corresponding front and top views.



Solution:

Question 3.
For the given solid, identify the front, side and top views and write it in the space provided.

Solution:

Question 4.
For each of the given solid, the three views are given. Identify for each solid the corresponding top, front and side views.



Solution:

Question 5.
For each given solid, identify the top view, front view and side view.


Solution:

Question 6.
Draw the front view, side view and top view of the given objects:


Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths