M.C.Q (1 Marks)

MCQ 2011 Mark

A circus tent is cylindrical up to a height of $4 m$ and conical above it. If its diameter is $105 m$ and its slant height is $40 m$, the total area of canvas required to built the tent is

✓
$7920 m ^2$
B
$7820 m ^2$
C
$9720 m ^2$
D
$2645 m ^2$

Answer

Correct option: A.

$7920 m ^2$

(a) : Area of canvas $=(2 \pi r h+\pi r l)$
$
=\left(2 \times \frac{22}{7} \times \frac{105}{2} \times 4+\frac{22}{7} \times \frac{105}{2} \times 40\right) m ^2=7920 m ^2
$

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MCQ 2021 Mark

The base radius of the cylinder is $1 \frac{2}{3}$ times its height. The cost of painting its $\text{C.S.A.}$ at $2$ paise $/ \ cm ^2$ is $₹\ 92.40$ . The volume of the cylinder is

✓
$80850 \ cm ^3$
B
$88850 \ cm ^3$
C
$80508 \ cm ^3$
D
None of these

Answer

Correct option: A.

$80850 \ cm ^3$

$r=\frac{5}{3} h, \text{C.S.A}. =2 \pi r h=2 \times \frac{22}{7} \times \frac{5}{3} h^2$
$\Rightarrow \frac{220}{21} h^2=\frac{9240}{2} $
$\Rightarrow h=21 \ cm , r=35 \ cm$
$\therefore V=\pi r^2 h=\frac{22}{7} \times 35 \times 35 \times 21=80850 \ cm ^3$

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MCQ 2031 Mark

The radii of the base of a cylinder and a cone are in the ratio $3: 4$ and their heights are in the ratio $2: 3$, then ratio of their volumes is

✓
$9: 8$
B
$9: 4$
C
$3: 1$
D
$27: 64$

Answer

Correct option: A.

$9: 8$

(a) : Let the radii of the cylinder and cone be $3 r$ and $4 r$ respectively and their heights be $2 h$ and $3 h$ respectively. Then,
$
\frac{\text { Volume of cylinder }}{\text { Volume of cone }}=\frac{\pi(3 r)^2 \times 2 h}{\frac{1}{3} \pi(4 r)^2 3 h}=\frac{54}{48}=\frac{9}{8}
$

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MCQ 2041 Mark

The ratio of the volumes of two spheres is $8: 27$. The ratio between their surface areas is

A
$2: 3$
B
$4: 27$
C
$8: 9$
✓
$4: 9$

Answer

Correct option: D.

$4: 9$

(d) : $\frac{\text { Volume of sphere with radius } r}{\text { Volume of sphere with radius } R}$
$
=\frac{\frac{4}{3} \pi r^3}{\frac{4}{3} \pi R^3}=\frac{8}{27} \Rightarrow \frac{r^3}{R^3}=\frac{8}{27} \Rightarrow\left(\frac{r}{R}\right)^3=\left(\frac{2}{3}\right)^3 \Rightarrow \frac{r}{R}=\frac{2}{3}
$
Ratio between their surface areas
$
=\frac{4 \pi r^2}{4 \pi R^2}=\frac{r^2}{R^2}=\left(\frac{r}{R}\right)^2=\left(\frac{2}{3}\right)^2=\frac{4}{9}
$

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MCQ 2051 Mark

The height of a cylinder is $14 \ cm$ and its curved surface area is $264 \ cm ^2$. The volume of the cylinder is

A
$296 \ cm ^3$
✓
$396 \ cm ^3$
C
$369 \ cm ^3$
D
$503 \ cm ^3$

Answer

Correct option: B.

$396 \ cm ^3$

$\text{C.S.A.} =2 \pi r h=2 \times \frac{22}{7} \times r \times 14=264\ ($given$)$
$\Rightarrow r=\frac{264}{88}=3 \ cm$
$\therefore$ Volume $=\pi r^2 h=\frac{22}{7} \times 3 \times 3 \times 14=396 \ cm ^3$

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MCQ 2061 Mark

The ratio of the total surface area to the lateral surface area of a cylinder with base radius $80 cm$ and height $20 cm$ is

A
$1: 2$
B
$2: 1$
C
$3: 1$
✓
$5: 1$

Answer

Correct option: D.

$5: 1$

(d) : $\frac{\text { Total surface area }}{\text { Lateral surface area }}=\frac{2 \pi r(h+r)}{2 \pi r h}$
$
=\frac{h+r}{h}=\frac{(20+80)}{20}=\frac{100}{20}=\frac{5}{1}
$
$\therefore \quad$ Required ratio is $5: 1$.

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MCQ 2071 Mark

The volume of a cube is $2744 \ cm ^3$. Its surface area is