- QUESTION
Ice-cream, completely filled in a cylinder of diameter 35 cm and height 32 cm, is to be served by completely filling identical disposable cones of diameter 4 cm and height 7 cm. The maximum number of cones that can be used in this way is
A)950
B)1000
C)1050
D)1100
Explanation
(C)
Given:
Diameter of cylinder = 35cm
Height of cylinder = 32cm
Diameter of cone = 4 cm
Height of cone = 7 cm
Formula used:
Volume of cylinder = pi * r ^ 2 * h
Volume of cone = 1/3 * pi * r ^ 2 * h
Calculation:
Radius of cylinder = 35/2 cm
Radius of cone = 4/2 = 2 cm
Now,
Let n persons can be served
Volume of the cylinder = n * (Volume of a disposable cone
= [πα (35/2) × (35/2) x 32]
= n x (π/3 × 4 × 7)
=n = 350 * 3 = 1050
QUESTION-2
Which two figures will have same area?
(A) Circle with diameter of 14 cm
(B) Rectangle with length 12 cm and breadth 10 cm.
(C) Rectangle with length 14 cm and breadth 11 cm.
(D) Square with side 12 cm
Choose the correct answer from the options given below :
A)A and B only
B)B and D only
C)A and C only
D)A and D only
Explanation
(C)
=A and C only
(A) Area of the circle with diameter \( 14 \) cm:
\[ \text{Area} = \pi \times \left( \frac{d}{2} \right)^2 \]
\[ \text{Area} = \pi \times \left( \frac{14}{2} \right)^2 = 49\pi \, \text{cm}^2 \]
(C) Area of the rectangle with length \( 14 \) cm and breadth \( 11 \) cm:
\[ \text{Area} = \text{length} \times \text{breadth} = 14 \times 11 = 154 \, \text{cm}^2 \]
You’re right; I made a mistake in my previous response. The correct comparison shows that the areas of options (A) and (C) are equal:
\[ 49\pi \, \text{cm}^2 = 154 \, \text{cm}^2 \]
So, the correct answer is option (C) – A and C only.
QUESTION-3
Given below are two statements
Statement I -The perimeter of a triangle is greater than the sum of its three medians
Statement II -In any triangle ABC, if D is any point on BC, then AB+BC+CA > 2 AD
In the light of the above statements, choose the correct answer from the options given below:
A)Both Statement I and Statement II are true
B)Both Statement I and Statement II are false
C)Statement I is true but Statement II is false
D)Statement I is false but Statement II is true
Explanation
(A)
=
Let A, BC be the triangle & D, E & F are midpoints
Now sum of two sides of a triangle is greater than twice the radius
So, AB + AC > 2AD
Same for
BC + AC > 2CF
BC + AB > 2BE
Odd above 3 equations
2(A.B+BC+AC)> 2(AD + BE + CF)
AB + BC + AC > AD + BE + CF
So, perimeters of triangle is greater than sum of its medians
Statement 1 is correct
D is a midpoint on BC means AD is a median
We know that,
Sum of two sides a triangle is greater the twice of the median
AB + AC > 2AD
Since BC is positive number
AB + AC + BC > 2AD
So, statement 2 is correct
= Both 1 & 2 are correct
Leave a Reply