Mensuration Model Questions Set 2 Practice Questions Answers Test with Solutions & More Shortcuts
Mensuration PRACTICE TEST [2 - EXERCISES]
Mensuration Model Questions Set 1
Mensuration Model Questions Set 2
Question : 11
ABCD is a quadrilateral such that BC = BA and CD > AD. Which one of the following is correct?
a) ∠BAD > ∠BCD
b) ∠BAD = ∠BCD
c) ∠BAD < ∠BCD
d) None of these
Answer »Answer: (a)
Construction : In quadrilateral ABCD, form A to C.
Now, in ΔABC
∵ AB = BC ...(Given)
∴ ∠BAC = ∠BCA
(angles opposite to equal side)
In ΔADC,
∵ CD > AD
∴ ∠DAC> ∠DCA
(since in a triangle, angle opposite to greater side is bigger than the angle opposite to smaller side)
On adding eqs. (i) and (ii), we get
∠BAD > ∠BCD
Question : 12
The length, breadth and height of a cuboid are in the ratio 1 : 2 : 3. The length, breadth and height of the cuboid are increased by 100%, 200% and 200%, respectively. Then, the increase in the volume of the cuboid will be
a) 12 times
b) 5 times
c) 6 times
d) 17 times
Answer »Answer: (d)
Let the length, breadth and height of the cuboid be x, 2x and 3x, respectively.
Therefore, volume = x × 2x × 3x = $6x^3$
New length, breadth and height = 2x, 6x and 9x, respectively.
New volume = $108x^3$
Thus, increase in volume = $(108 – 6)x^3 = 102x^3$
${\text"Increase in volume"}/{\text"Original volume"} = {102x^3}/{6x^3}$ = 17
Question : 13
Two circles touch each other internally. Their radii are 4 cm and 6 cm. What is the length of the longest chord of the outer circle which is outside the inner circle?
a) 6 $√3$ cm
b) 4 $√2$ cm
c) 4 $√3$ cm
d) 8 $√2$ cm
Answer »Answer: (d)
Let O is centre of big circle, and O' is centre of smaller circle. Both are touch internally each other.
OA = 6 cm O'A = 4cm
Here PR is longest chord of big circle
P.S = ${PR}/2$
OS = AS – OA
= 8 – 6 = 2 cm.
In ΔPSO
$(PS)^2 + (OS)^2 = (OP)^2$
⇒ $(PS)^2 + (2)^2 = (6)^2$
PS = $√{36 - 4} = √{32} = 4 √2$
Now,
PS = ${PR}/2$
PR = 2 × PS
= 2 × $4 √2 = 8 √2$
Question : 14
Let LMNP be a parallelogram and NR be perpendicular to LP. If the area of the parallelogram is six times the area of ΔRNP and RP = 6 cm what is LR equal to?
a) 9 cm
b) 15 cm
c) 12 cm
d) 8 cm
Answer »Answer: (c)
Area of parallelogram = 6 × Area of ΔNPR
∴ NR × PL= 6 × $1/2$ × NR × PR
⇒ PL = 3PR (here, PL = PR + RL)
⇒ PR + RL= 3PR
⇒ RL= 2PL = 2 × 6 = 12 cm
Question : 15
In the figure given, ∠B = 38°, AC = BC and AD = CD. What is ∠D equal to?
a) 38°
b) 26°
c) 28°
d) 52°
Answer »Answer: (c)
Given, AC = BC
In ΔABC, ∠ABC = ∠CAB
∠ABC = ∠CAB = 38° (∴ AC = BC)
∠ACB = 180° – (∠ABC + ∠CAB)
= 180° – (38° + 38°) = 180° – 76° = 104°
In ΔACD, ∠ACD = 180° – 104° = 76°
and ∠ACD = ∠CAD = 76°
(∵ CD = AD)
∴ ∠ADC = 180° – (∠ACD + ∠CAD)
= 180° – (76° + 76°) = 28°
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