Mathematics - Class X Question Paper - Central Board Of Secondary Education Page 16

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Q. NO.
VALUE POINTS
Marks
OR
Let A and B are two positions of the aeroplane. Let AB = d
Correct fig
1
OL
1
∴
= cot° 60° Ü OL = 1.5 (
) = (0.5) œ 3 km
1½
AL
œ 3
OM
= cot 30° Ü OM = (1.5) (œ 3) km
1½
BM
∴ d = OM — OL = (1.5) œ 3 — (0.5) œ 3 = œ 3 km
1
œ 3
∴ speed =
Distance
= 240 œ 3 km/hr
=
1
15
time
3600
or 415.68 km/hr
[
]
1
2
π(3)².4 +
π(3)³
Q24. Volume of toy =
cm³
1
3
3
= [12π + 18π] cm³
½
= 30 x 3.14 = 94.20 cm³
1
slant height of cone = œ 3² + 4² = 5 cm
1
4 cm
Total surface Area
3 cm
= [π(3) (5) + 2π (3²)] cm²
1
= (15π + 18π) cm²
½
= 33 (3.14) = 103.62 cm²
1
OR
Let ABCD be the bucket which is the frustrum
of a cone with vertex O (as in fig.)
½
9 cm
Let ON = x
M
D
C
x
3
∆ ONB ~ ∆ OMC ∴
Ü x = 4
=
1
x+8
9
∴ height of cone = 8 + 4 = 12 cm
½
8 cm
Volume of bucket = [π(9)².12 — π(3)².4] cm³
1
N
3 cm
= 312 π cm³
A
B
Slant height of cone of radius 9cm = 9² + 12² cm
½
∴ L = 15 cm
½
Slant height of cone of radius 3cm = 3² + 4² cm
l = 5 cm
½
Area of the copper sheet used to form bucket
O
= [π(9) (15) - π(3) (5) + π(3)² cm²
1
129π cm²
½
151

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