How Big? How Heavy? Test 1

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How Big? How Heavy? Test 1

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Question 1
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If one square is $$1$$ unit cube, then the volume of the given object is:

A
$$18$$ unit cubes

B
$$20$$ unit cubes

C
$$22$$ unit cubes

D
$$24$$ unit cubes

Solution

Let the smallest cube i.e one square is of $$1$$ unit cube.
The total number of unit cubes in the figure $$=5\times 2\times2 +2=22$$
Thus, the volume of the given object is $$22$$ unit cubes.
Question 2
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If weight of $$1$$ mango is $$250$$ gms, then calculate the weight of $$16$$ mangoes. (Write your answer in kilograms)

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

Weight of $$1$$ mango $$=250 $$ $$\text{gram}$$

Weight of $$16$$ mangoes $$=250 \times 16\ \text{gram} = 4000$$ $$\text{gram}$$

We know that

$$1$$ $$\text{kg} =1000$$ $$\text{gram}$$

$$1$$ $$\text{gram} =\dfrac1{1000}$$ $$\text{kg}$$

We have to convert $$4000$$ $$\text{gram}$$ to $$\text{kg}$$:

$$4000$$ $$\text{gm} =\dfrac{1}{1000} \times 4000$$ $$\text{kg}$$

$$ =\dfrac{4000}{1000} $$ $$\text{kg}$$

$$=4$$ $$\text{kg}$$

So, option $$D$$ is correct.
Question 3
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Weight of $$\triangle$$ and $$\square$$ together is $$28$$ and weight of $$\square =13$$. Then the weight of $$\triangle$$ is ?

A
$$15$$

B
$$14$$

C
$$13$$

D
$$12$$

Solution

Total weight of $$\Delta $$ and $$\square$$ is $$28$$

or $$\Delta + \square$$ $$=28$$ ........................(1)

Given : weight of $$\square$$ is $$13$$ or $$\square$$ $$=13$$

Now from equation (1)

$$\Delta + 13 $$ $$=28$$

$$\Rightarrow \Delta $$ $$=28-13$$

$$\Rightarrow \Delta $$ $$=15$$

So, weight of $$\Delta$$ is $$15$$

Hence, option A is correct.
Question 4
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A cubical block of metal weighs $$6$$ pounds. How much will another cube of the same metal weigh if its sides are twice as long?

A
$$48$$

B
$$32$$

C
$$24$$

D
$$18$$

E
$$12$$

Solution
Question 5
1 / -0

If $$15.5$$ litres of refined oil costs Rs. $$1063.30$$, what is the cost of $$1$$ litre of refined oil?

A
Rs. $$68.60$$

B
Rs. $$75.95$$

C
Rs. $$70.89$$

D
Rs. $$62.55$$

Solution

Given that $$15.5$$ litres refined oil costs $$\rightarrow$$ $$1063.30$$ Rs
Cost of $$1$$ litre refined oil will be $$\dfrac {1063.30}{15.5}=$$ $$68.60$$
Thus $$1$$ litre refined oil costs Rs. $$68.60$$.
Hence, option A is correct.
Question 6
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How many cubes are in this rectangular prism (cuboid)? And hence, calculate the volume of the cuboid.
(Volume of $$1$$ cube $$=1$$ cubic units)

A
$$12$$ cubic units

B
$$24$$ cubic units

C
$$48$$ cubic units

D
$$54$$ cubic units

Solution

Number of cubes$$=48$$
Volume of cuboid$$=48\times $$ volume of each cube$$=48\times 1=48$$ cubic units.
Question 7
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Calculate the volume of an object given in the figure, where each small cubes has a volume $$1$$ cubic units.

A
$$16$$ cubic units

B
$$32$$ cubic units

C
$$48$$ cubic units

D
$$52$$ cubic units

Solution

In given figure, the first two layers from the ground have $$16(4\times 4)$$ cube. The remaining two layers have $$10$$ cubes each.
Total number of cubes
$$=2\times 10+2\times 16=40+12=52$$ cubes

Since, the volume of $$1$$ small cube $$=1\ cubic\ units$$

Hence, the required volume
$$=52\times 1=52\ cubic\ units$$
Question 8
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Which of the following object has greater volume?

A
Figure I

B
Figure II

C
Both have equal volume

D
Can't compare
Question 9
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A rectangular tank whose length and breadth are $$2.5m$$ and $$1.5m$$ respectively is half full of water. If $$450$$ litre more water is poured into the tank, what is the height through which water level further goes up?

A
$$20cm$$

B
$$18cm$$

C
$$15cm$$

D
$$200cm$$

Solution
Question 10
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How many small cubes are there in each cuboid respectively?

A
$$10,12$$

B
$$12,10$$

C
$$5,6$$

D
$$6,5$$

Solution

The total number of small cubes in figure 1 is $$2\times 2\times 3=12$$
The total number of small cubes in figure 2 is $$2\times 5=10$$
Hence, the answer is $$12,10$$.