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Q:

The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.
What is the surface area of the cuboid?

A) 288 sq.cm	B) 216 sq.cm
C) 144 sq.cm	D) Cannot be determined due to insufficient data

Answer & Explanation Answer: A) 288 sq.cm

Explanation:

Let lengths, breadth and height of cuboid be l, b and h respectively

According to question

l+b+h = 22cm......(i)

and

√(l^2+b^2+h^2) = 14cm .....(ii)

Surface area of cuboid = 2(lb+bh+lh)

Squaring eq (i) gives

l^{2} + b^{2} + h^{2}

+ 2(lb+bh+lh) = 484

Substituting l^2+b^2+h^2 from eq (i)

2(lb+bh+lh) = 484 -196 = 288 sq.cm

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Q:

An equilateral triangle ABC is inscribed in a circle of radius 20√3.
The centroid of the triangle ABC is at a distance d from the vertex A. What is d equal to ?

A) 15 cm	B) 20 cm
C) 20√3 cm	D) 30√3 cm

Answer & Explanation Answer: C) 20√3 cm

Explanation:

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Q:

An equilateral triangle ABC is inscribed in a circle of radius 20√3.
What is the length of the side of the triangle?

A) 30 cm	B) 40 cm
C) 50 cm	D) 60 cm

Answer & Explanation Answer: D) 60 cm

Explanation:

Radius of circumcircle of an equilateral triangle = side /√3

R = a/√3

a = R√3 = 20√3 *√3 = 60cm

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Q:

ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right –angel
What is the difference between perimeter of triangle ABC and perimeter of triangle ADC?

A) 4 cm	B) 5 cm
C) 6 cm	D) 7 cm

Answer & Explanation Answer: C) 6 cm

Explanation:

Perimeter of triangle ABC – Perimeter of triangle ADC = (9+40+41) - (15+28+41) = 6 cm

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Q:

ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right –angel
What is the area of quadrilateral ABCD?

A) 300 SQ.CM	B) 306 SQ.CM
C) 312 SQ.CM	D) 316 SQ.CM

Answer & Explanation Answer: D) 316 SQ.CM

Explanation:

Area of quadrilateral ABCD = area of triangle ADC + area of triangle ABC

= 126 + ½ * 9 * 40 = 306

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Q:

ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right –angel.
What is the area of triangle ADC?

A) 126 SQ.CM	B) 124 SQ.CM
C) 122 SQ.CM	D) 120 SQ.CM

Answer & Explanation Answer: A) 126 SQ.CM

Explanation:

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Q:

A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.

Consider the following statements:

1) The surface area of the sphere is √5 Times the curved surface area of the cone.

2) The surface area of the cube is equal to the curved surface area of the cylinder. Which of the above statements is/are correct?

A) 1 only	B) 2 only
C) Both 1 and 2	D) Neither 1 nor 2

Answer & Explanation Answer: D) Neither 1 nor 2

Explanation:

The top view of the given assembly will look like the figure above

Outermost is the sphere. Inside that there is a cube and within that there is a cone and cylinder with same radius.

Here side of cube = a

Diameter of Sphere = body diagnol = √3 a

Radius of sphere = √3 a/2 =r1

Height of Cylinder = Height of cone = side of cube = a =h

Radius of cylinder = Radius of cone = side of cube/2 = a/2 =r2(as shown in the figure)

Thus neither 1 nor 2 are true

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Q:

A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.

What is the ratio of the volume of the cube to that of the cylinder ?

A) 4 : 3	B) 21 : 16
C) 14 : 11	D) 45 : 32

Answer & Explanation Answer: C) 14 : 11

Explanation:

The top view of the given assembly will look like the figure above

Outermost is the sphere. Inside that there is a cube and within that there is a cone and cylinder with same radius.

Here side of cube = a

Diameter of Sphere = body diagnol = √3 a

Radius of sphere = √3 a/2 =r1

Height of Cylinder = Height of cone = side of cube = a =h

Radius of cylinder = Radius of cone = side of cube/2 = a/2 =r2(as shown in the figure)

\frac{Vcube}{Vcylinder} = \frac{a^{3}}{{πr}_{2}^{2} h} = 14 / 11

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