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MATHS MCQ

Mensuration · ICSE STD 8 (ICSE - English Medium). 15 questions.

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15 questions · timed · auto-graded

MCQ 11 Mark
If the radius of a cylinder is doubled and height is halved, then new volume is
  • A
    same
  • ✓
    $2$ times
  • C
    $4$ times
  • D
    $8$ times
Answer
Correct option: B.
$2$ times
Let radius $=r$
and height $=h$
Then volume $=\pi r^2 h$
If radius is doubled
i. e. $2 r$ and height is halved
i.e. $\frac{h}{2}$,
then Volume $=\pi(2 r)^2 \times \frac{h}{2}$
$=\pi \times 4 r^2 \times \frac{h}{2}$
$=2 \pi r^2 h$
$\therefore$ Its volume is doubled $(2$ times$)$
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MCQ 21 Mark
Volume of a cylinder is $1848\  cm ^2$. If the diameter of its base is $14\  cm$, then the height of the cylinder is
  • ✓
    $12 \ cm$
  • B
    $6 \ cm$
  • C
    $3 \ cm$
  • D
    none of these
Answer
Correct option: A.
$12 \ cm$
Volume of a cylinder $=1848 \ cm ^2$
Diameter of base $=14 \ cm$
$\therefore$ Radius $(r)=\frac{14}{2}=7 \ cm$
$V=\pi r^2 h$
$\therefore$ Height $=\frac{ V }{\pi r^2}$
$=\frac{1848 \times 7}{22 \times 7 \times 7}=12 \ cm$
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MCQ 31 Mark
If the dimensions of a rectangular room are $10\ m \times 12\ m \times 9\ m,$ then the cost of painting its four walls at the rate of $₹\ 8$ per $m^2$ is
  • A
    $₹\ 3186$
  • B
    $₹\ 3618$
  • ✓
    $₹\ 3168$
  • D
    none of these
Answer
Correct option: C.
$₹\ 3168$
Dimensions of a room $= 10\ m\times 12 \times 9\ m$
Area of $4$ walls $= 2(l + b)h$
$= 2(10 + 12) \times 9 = 2 \times 22 \times 9\ m^2$
$= 396 \ cm^2$
Cost of painting $= ₹\ 8$ per $m^2$
$\therefore$ Total cost $= 396 \times 8 = ₹\ 3168$
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MCQ 41 Mark
If the length of side of a cube is doubled, then the ratio of volumes of new cube and original cube is
  • A
    $1: 2$
  • B
    $2: 1$
  • C
    $4: 1$
  • ✓
    $8: 1$
Answer
Correct option: D.
$8: 1$
Let original side of a cube $=x$
Then volume $=x^3$
If edge is doubled i.e. edge $=2 x$
Then volume $=(2 x)^3=8 x^3$
$\therefore$ Ratio between new cube and original cube
$=8 x^3: x=8: 1$
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MCQ 51 Mark
If the lateral surface area of a cube is $100 \ cm ^2$, then its volume is
  • A
    $25 \ cm ^3$
  • ✓
    $125 \ cm ^3$
  • C
    $625 \ cm ^3$
  • D
    none of these
Answer
Correct option: B.
$125 \ cm ^3$
Lateral surface area of a cube $=4($ Edge $)^2=100 \ cm ^2$
$\therefore 4 \times($ edge $)^2=100$
$\Rightarrow($ edge $)^2=\frac{100}{4}=25=(5)^2$
$\therefore$  Edge of cube $ =5 \ cm$
Volume $ =($ edge $)^3=(5)^3=125 \ cm ^3$
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MCQ 61 Mark
If the volume of a cube is $729 \ cm ^3$, then its surface area is
  • ✓
    $486 \ cm ^2$
  • B
    $324 \ cm ^2$
  • C
    $162 \ cm ^2$
  • D
    none of these
Answer
Correct option: A.
$486 \ cm ^2$
Volume of a cube $=729 \ cm ^3$
$V =($ Side $)^3$
$\therefore$ Side $($edge$) =\sqrt[3]{729}$
$=\sqrt[3]{9 \times 9 \times 9}$
$=9 \ cm$
Then surface area $=6 \times(\text { side })^2$
$=6 \times(9)^2=6 \times 81 \ cm ^2$
$=486 \ cm ^2$
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MCQ 71 Mark
Area of a rhombus is $90\  cm ^2$. If the length of one diagonal is $10\  cm$ then the length of other diagonal is
  • ✓
    $18\  cm$
  • B
    $9\  cm$
  • C
    $36\  cm$
  • D
    $4.5\  cm$
Answer
Correct option: A.
$18\  cm$
Area of a rhombus $=90\  cm ^2$
Length of one diagonal $=10\  cm$
Area of rhombus $=\frac{1}{2} \times d_1 \times d_2$
$\therefore$ Length of second diagonal $=\frac{A \times 2}{d_1}$
$=\frac{90 \times 2}{10}=18\  cm$
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MCQ 81 Mark
If the length of a diagonal of a quadrilateral is $10 \ cm$ and lengths of the perpendiculars on it from opposite vertices are $4 \ cm$ and $6 \ cm,$ then area of quadrilateral is
  • A
    $100 \ cm ^2$
  • B
    $200 \ cm ^2$
  • ✓
    $50 \ cm ^2$
  • D
    none of these
Answer
Correct option: C.
$50 \ cm ^2$
Length of a diagonal of a quadrilateral $=10 \ cm$ and lengths of perpendicular on it from the opposite vertices $=4 \ cm$ and $6 \ cm$
$\therefore \text { Area }=\frac{1}{2}(4+6) \times 10 \ cm ^2$
$=\frac{1}{2} \times 10 \times 10$
$=50 \ cm ^2$
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MCQ 91 Mark
If the lengths of diagonals of a rhombus is doubled, then area of rhombus will be
  • A
    doubled
  • B
    tripled
  • ✓
    four times
  • D
    remains same
Answer
Correct option: C.
four times
Area of rhombus $1=\frac{1}{2} \times d_1 \times d_2$
Now the diagonals are doubled
Area of rhombus $=\frac{1}{2} \times 2 d _1 \times 2 d _2=2 d _1 d _2$
with doubled diagonals.
Lengths of diagonals are doubled, then the area will be four times. 
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MCQ 101 Mark
Area of a rhombus whose diagonals are $8\  cm$ and $6\  cm$ is
  • A
    $48 \ cm ^2$
  • ✓
    $24 \ cm ^2$
  • C
    $12 \ cm ^2$
  • D
    $96 \ cm ^2$
Answer
Correct option: B.
$24 \ cm ^2$
Area of rhombus $=\frac{d_1 \times d_2}{2}=\frac{8 \times 6}{2}$ $=\frac{48}{2}=24\  cm ^2$
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MCQ 111 Mark
If the area of a trapezium is $64\  cm ^2$ and the distance between parallel sides is $8\ cm$, then sum of its parallel sides is
  • A
    $8 \ cm$
  • B
    $4\  cm$
  • C
    $32\  cm$
  • ✓
    $16\  cm$
Answer
Correct option: D.
$16\  cm$
Area of trapezium $=64 \ cm ^2$
Distance between parallelogram $(h)=8 \ cm$
Area of trapezium $=\frac{1}{2} \times($Sum of $\| g m$ sides$) \times h$
Sum of parallel lines $=\frac{ A \times 2}{h}$
$=\frac{64 \times 2}{8}=16 \ cm$
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MCQ 121 Mark
If $d$ is the diameter of a circle, then its area is
  • A
    $\pi d^2$
  • B
    $\frac{\pi d^2}{2}$
  • ✓
    $\frac{\pi d^2}{4}$
  • D
    $2 \pi d^2$
Answer
Correct option: C.
$\frac{\pi d^2}{4}$
$d$ is the diameter a circle
$\therefore$ Radius $=r=\frac{d}{2}$
Area $=\pi r^2=\pi\left(\frac{d}{2}\right)^2$
$=\pi \frac{d^2}{4}$
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MCQ 131 Mark
Area of a parallelogram is $48\  cm ^2$. If its height is $6\  cm$ then its base is
  • ✓
    $8\  cm$
  • B
    $4\  cm$
  • C
    $16\  cm$
  • D
    none of these
Answer
Correct option: A.
$8\  cm$
Area of parallelogram $=48 \ cm ^2$
Height $=6 \ cm$
Area of $\| gm =$ Base $\times$ Height
Base $=\frac{ A }{h}=\frac{48}{6}=8\ \ cm$
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MCQ 141 Mark
If the perimeter of a square is $80 \ cm,$ then its area is
  • A
    $800 \ cm ^2$
  • B
    $600 \ cm ^2$
  • ✓
    $400 \ cm ^2$
  • D
    $200 \ cm ^2$
Answer
Correct option: C.
$400 \ cm ^2$
Perimeter of a square $=80 \ cm$
Perimeter of square $=4($Side$)$
$\therefore$ Side $=\frac{\text { Perimeter }}{4}$
$\therefore$ Side $=\frac{80}{4}=20 \ cm$
 Area $=($side$)^2$
$=(20)^2$
$=400 \ cm ^2$
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MCQ 151 Mark
Area of a triangle is $30 \ cm^2$. If its base is $10 \ cm,$ then its height is
  • A
    $5\ cm$
  • ✓
    $6\ cm$
  • C
    $7\ cm$
  • D
    $8\ cm$
Answer
Correct option: B.
$6\ cm$
Area of a triangle $=30 \ cm ^2$
Base $=10 \ cm$
Area $=\frac{1}{2} \times$ Base $\times$ Height 
Height $=\frac{A \times 2}{B}=\frac{30 \times 2}{10}=6 \ cm$ 
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