RBSE Class 7 Maths Important Questions Chapter 15 Visualising Solid Shapes

Rajasthan Board RBSE Class 7 Maths Important Questions Chapter 15 Visualising Solid Shapes Important Questions and Answers.

RBSE Class 7 Maths Chapter 15 Important Questions Visualising Solid Shapes

Multiple Choice Questions

Question 1.
Number of edges in a cube is :
(a) 12
(b) 8
(c) 6
(d) 4
Answer:
(a) 12

Question 2.
Number of vertices in a cylinder is :
(a) 2
(b) 4
(c) 1
(d) 0
Answer:
(d) 0

Question 3.
Number of faces in a cone is :
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(b) 2

Question 4.
Which of the following solids has no vertices?
(a) Cone
(b) Cylinder
(c) Cube
(d) Pyramid
Answer:
(b) Cylinder

Question 5.
Which of the following solids has only one face?
(a) Cone
(b) Cylinder
(c) Sphere
(d) Pyramid
Answer:
(c) Sphere

Fill in the blanks

Question 1.
Solid objects have definite ___________ and ___________ .
Answer:
shape, size ,

Question 2.
Line joining two comers of a solid is known as ____________ .
Answer:
edge

Question 3.
A cone has ___________ vertex.
Answer:
one

Question 4.
The net for a cylinder without top and bottom is a ___________ .
Answer:
rectangle

Question 5.
____________ prism is called a cube.
Answer:
square

State whether True or False

Question 1.
A sphere has no vertex.
Answer:
True

Question 2.
A sphere has one plane surface.
Answer:
False

Question 3.
A cuboid has 6 faces, 12 edges and 8 vertices.
Answer:
True

Question 4.
We use squared paper for oblique sketches of solid objects.
Answer:
True

Question 5.
According to Euler's formula F - E + V = 4.
Answer:
False

Brain-Teasers

Question 1.
Solve the number riddles :

(i) Tell me who I am! Who I am!
Take away from me the number eight, Divide further by a dozen to come up with A full team for a game of cricket!
(ii) Add four to six times a number,
To get exactly sixty four!
Perfect credit is yours to ask for
If you instantly tell the score!
Answer:
(i) Let I be x. Then according to the question,
⇒ \(\frac{x-8}{12}\) = 11
⇒ x - 8 = 12 × 11
(∵ There are 11 players in a full team of cricket.)
⇒ x - 8 = 132
⇒ x = 132 + 8
⇒ x = 140
Hence, I am the number 140.

(ii) Let the number be x.
Then, according to the question,
6x + 4 = 64
⇒ 6x = 64 - 4
⇒ 6x = 60
⇒ x = \(\frac{60}{6}\)
⇒ x = 10
Hence, the required number is 10.

Question 2.
Solve the teasers :
(i) There was in the forest an old Peepal tree The grand tree had branches ten and three On each branch there lived birds fourteen Sparrows brown, crows black and parrots green !
Twice as many as the parrots were the crows And twice as many as the crows were the sparrows!
We wonder how many birds of each kind Aren’t you going to help us find?
(ii) I have some five-rupee coins and some two-rupee coins. The number of two-rupee coins is twice the number of five rupee coins. The total money I have is 108 rupees. So how many five-rupee coins do I have? And how many two rupee coins?
Answer:
(i) Number of branches on the tree = 10 + 3 = 13
Number of birds on each branch = 14
∴ Total number of birds = 13 × 14 = 182
Let the number of parrots be x.
Then, number of crows = 2x and number of sparrows = 2(2x) = 4x
∴ According to the question,
x + 2x + 4x = 182 ⇒ 7x = 182
⇒ x = \(\frac{182}{7}\) ⇒ x = 26
x = 26, 2x = 52, 4x = 104
Hence, parrots = 26, Crows = 52, Sparrows = 104

(ii) Let five-rupee coins = x
Then number of two-rupee coins = 2x
Total Money = 5x + 2 × 2x
= 5x + 4x = 9x
But Total Money = ₹ 108
∴ 9x = 108
x = \(\frac{108}{9}\) = 12
Hence, five rupee coins = 12 and two rupee coins = 2 × 12 = 24

Question 3.
I have 2 vats each containing 2 mats. 2 cats sat on each of the mats.
Each cat wore 2 funny old hats. On each hat lay 2 thin rats. On each rat perched 2 black bats. How many things are in my vats?
Answer:
Each vat containing 2 mats, so total mats = 2 × 2 = 4
Total number of cats = 4 × 2 = 8
Each cat wore 2 hats, so total hats = 8 × 2 = 16
On each hat there are two thin rats.
So, total number of rats = 16 × 2 = 32
Total number of black bats = 32 × 2 = 64
So, total things in vats = 4 + 8 + 16 + 32 + 64 = 124

Question 4.
Twenty-seven small cubes are glued together to make a big cube. The exterior of the big cube is painted yellow in colour. How many among each of the 27 small cubes would have been painted yellow on
(i) only one of its faces?
(ii) two of its faces?
(iii) three of its faces?
Answer:
(i) Number of cubes with 1 face painted = Cubes on the faces (except on the edges and the corners) = (n - 2)² × 6 = 6
(ii) Number of cubes with 2 faces painted = Along the edges of the larger cube
= (n - 2) × 12 = 12
(iii) Number of cubes with 3 faces painted = All the corner cubes = 8

Question 5.
Rahul wanted to find the height of a tree in his garden. He checked the ratio of his height to his shadow's length. It was 4:1. He then measured the shadow7 of the tree. It was 15 feet. So what w as the height of the tree?
Answer:
Let height of the tree be x feet.
Since, the ratio of his height to his shadow will be equal to the ratio of tree to shadow of tree.
∴ 4 : 1 :: x : 15
⇒ x = 15 × 4 = 60 feet

Question 6.
A woodcutter took 12 minutes to make 3 pieces of a block of wood. How much time would be needed to make 5 such pieces?
Answer:
He make only 2 cuts to get 3 peices.
Time taken to break wood once = \(\frac{\text { Total time }}{2}\)
= \(\frac{12}{2}\) minutes = 6 minutes
5 pieces are got by making just 4 cuts,
So time time taken is = 6 × 4
= 24 minutes

Question 7.
A cloth shrinks 0.5% when washed. What fraction is this?
Answer:
Cloth shrinkage = 0.5%
Fraction = \(\frac{0.5}{100}\) = \(\frac{5}{1000}\) = \(\frac{1}{200}\)

Question 8.
Smita's mother is 34 years old. Two years from now mother's age will be 4 times Smita's present age. What is Smita's present age?
Answer:
Let Smita's present age = x years.
Smita’s mother age = 34 years So, after two year Simta’s age = (x + 2) years and his mother’s age = (34 + 2) years = 36 years
According to question
4 (x + 2) = 36
or (x + 2) = 9
x = 9 - 2 = 7
Hence, Simita’s present age 7 years.

Question 9.
Maya, Madhura and Mohsina are friends studying in the same class. In a class test in geography, Maya got 16 out of 25. Madhura got 20. Their average score was 19. How much did Mohsina score?
Answer:
Let Mohsina scored x marks.
Their average score = \(\frac{x+16+20}{3}\)
\(\frac{x+16+20}{3}\) = 19
⇒ x + 36 = 57
⇒ x = 57 - 36 = 21