Volume And Surface Area

What is the capacity of the cylindrical tank?
I.	The area of the base is 61,600 sq. cm.
II.	The height of the tank is 1.5 times the radius.
III.	The circumference of base is 880 cm.

A:

Only I and II

B:

Only II and III

C:

Only I and III

D:

Any two of the three

Answer: E

Capacity = r²h.

I gives, r² = 61600. This gives r.

II gives, h = 1.5 r.

Thus, I and II give the answer.

Again, III gives 2r = 880. This gives r.

So, II and III also give the answer.

Correct answer is (E).

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What is the volume of a cube?
I.	The area of each face of the cube is 64 square metres.
II.	The length of one side of the cube is 8 metres.

A:

I alone sufficient while II alone not sufficient to answer

B:

II alone sufficient while I alone not sufficient to answer

C:

Either I or II alone sufficient to answer

D:

Both I and II are not sufficient to answer

Answer: C

Let each edge be a metres. Then,

I. a² = 64 a = 8 m Volume = (8 x 8 x 8) m³ = 512 m³.

Thus, I alone gives the answer.

II. a = 8 m Volume = (8 x 8 x 8) m³ = 512 m³.

Thus, II alone gives the answer.

Correct answer is (C).

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What is the height of a circular cone?
I.	The area of that cone is equal to the area of a rectangle whose length is 33 cm.
II.	The area of the base of that cone is 154 sq. cm.

A:

I alone sufficient while II alone not sufficient to answer

B:

II alone sufficient while I alone not sufficient to answer

C:

Either I or II alone sufficient to answer

D:

Both I and II are not sufficient to answer

Answer: D

II gives the value of r.

But, in I, the breadth of rectangle is not given.

So, we cannot find the surface area of the cone.

Hence, the height of the cone cannot be determined.

Correct answer is (D).

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What is the capacity of a cylindrical tank?
I.	Radius of the base is half of its height which is 28 metres.
II.	Area of the base is 616 sq. metres and its height is 28 metres.

A:

I alone sufficient while II alone not sufficient to answer

B:

II alone sufficient while I alone not sufficient to answer

C:

Either I or II alone sufficient to answer

D:

Both I and II are not sufficient to answer

Answer: C

I gives, h = 28 m and r = 14.

Capacity = r²h, which can be obtained.

Thus, I alone gives the answer.

II gives, r² = 616 m² and h = 28 m.

Capacity = (r² x h) = (616 x 28) m³.

Thus, II alone gives the answer.

Correct answer is (C).

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Is a given rectangular block, a cube?
I.	At least 2 faces of the rectangular block are squares.
II.	The volume of the block is 64.

A:

I alone sufficient while II alone not sufficient to answer

B:

II alone sufficient while I alone not sufficient to answer

C:

Either I or II alone sufficient to answer

D:

Both I and II are not sufficient to answer

Answer: D

I gives, any two of l, b, h are equal.

II gives, lbh = 64.

From I and II, the values of l, b, h may be (1 ,1 , 64), (2 ,2 ,16), (4, 4, 4).

Thus, the block may be a cube or cuboid.

Correct answer is (D).

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Questions for: Volume And Surface Area