1 Marks Question

Question 11 Mark

How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?

Answer

Diameter = 10.5 cm.
$\therefore$ Radius (r) =$10.5\over2$=5.25 cm
$\therefore$ Amount of milk = ${2\over3}\pi r^3$
$={2\over3}\times{22\over7}\times(5.25)^3\ cm^3$
= 303 cm³ = 0.303 l

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Question 21 Mark

Find the amount of water displaced by a solid spherical ball of diameter 0.21 m.

Answer

Diameter = 0.21 m
∴ Radius (r) = ${0.21}\over2$m = 0.105 m
∴ Amount of water displaced = ${4\over3}\pi r^3$
$={4\over3}\times{22\over7}\times(0.105)^3=0.004851\ m^3$

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Question 31 Mark

Find the amount of water displaced by a solid spherical ball of diameter 28 cm.

Answer

Diameter = 28 cm
∴ Radius (r) =$28\over2$ cm = 14 cm
∴ Amount of water displaced = ${4\over3}\pi r^3$
$={4\over3}\times{22\over7}\times(14)^3={34496\over3}\ cm^3=11498{2\over3}\ cm^3$

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Question 41 Mark

Find the volume of a sphere whose radius is 0.63 m.

Answer

r = 0.63 m
∴ volume =${4\over3}\pi r^3$
$={4\over3}\times{22\over7}\times(0.63)^3=1.05\ m^3$

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Question 51 Mark

Find the volume of a sphere whose radius is 7 cm.

Answer

r = 7 cm
∴ Volume = ${4\over3}\pi r^3$
$={4\over3}\times{22\over7}\times(7)^3={4312\over3}\ cm^3=1437{1\over3}\ cm^3$

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Question 61 Mark

A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm³) is needed to fill this capsule?

Answer

Diameter of the capsule = 3.5 mm
$\therefore$ Radius of the capsule (r) = $3.5\over2$ mm = 1.75 mm
$\therefore$ Capacity of the capsule = ${4\over3}\pi r^3$
$={4\over3}\times{22\over7}\times(1.75)^3\ mm^3$
= 22.46 mm³
$\therefore$ 22.46 mm³ of medicine is needed to fill this capsule.

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Question 71 Mark

Find the volume of the right circular cone with radius 3.5 and height 12 cm.

Answer

r = 3.5 cm, h = 12 cm.
∴ Volume of the right circular cone $={1\over3}\pi r^2h$
$={1\over3}\times{22\over7}\times(3.5)^2\times12$ = 154 cm³

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Question 81 Mark

Find the volume of the right circular cone with radius 6 cm and height 7 cm.

Answer

r = 6 cm, h = 7 cm
∴ Volume of the right circular cone = ${1\over3}\pi r^2h$
$={1\over3}\times{22\over7}\times(6)^2\times7$ = 264 cm³

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Question 91 Mark

A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.

Answer

Inner radius of bowl $\left( r \right)$ = 5 cm
Thickness of steel $\left( t \right)$ = 0.25 cm
$\therefore $ Outer radius of bowl (R) = $r+t$ = 5 +0.25 = 5.25 cm
$\therefore $ Outer curved surface area of bowl = $2\pi {{\text{R}}^{2}}$= $2\times \frac{22}{7}\times 5.25\times 5.25$
= $2\times \frac{22}{7}\times \frac{21}{4}\times \frac{21}{4}$
= $\frac{693}{4}$
$=\text{ }173.25\text{ }c{{m}^{2}}$

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Question 101 Mark

Find the total surface area of a hemisphere of radius 10 cm.

Answer

r = 10 cm
Total surface area of the hemisphere = $3\pi r^2$
= 3 × 3.14 × (10)² = 942 cm²

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Question 111 Mark

Find the surface area of a sphere of diameter 3.5 cm.

Answer

Diameter = 3.5 cm
∴ Radius (r) = $3.5\over2$ cm = 1.75 cm
Surface area of sphere =^{$4\pi r^2$}
= 4×$22\over7$ × (1.75)² = 38.5 cm²

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Question 121 Mark

Find the surface area of a sphere of diameter 21 cm.

Answer

Diameter = 21 cm
∴ Radius (r) = $21\over2$ cm
Surface area of sphere =^{$4\pi r^2$}
= $4\times{22\over7}\times({21\over2})^2$

= $4\times{22\over7}\times{21\over2}\times{21\over2}$

=1386 cm²

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Question 131 Mark

Find the surface area of a sphere of diameter 14 cm.

Answer

Diameter = 14 cm
∴ Radius (r) = $14\over2$ cm = 7 cm
Surface area of sphere = ^{$4\pi r^2$}
= 4×$22\over7$ × (7)² = 616 cm²

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Question 141 Mark

Find the surface area of a sphere of radius 14 cm.

Answer

r = 14 cm
Surface area of a sphere =$4\pi r^2$
^{$=4\times{22\over7}\times(14)^2$}
$=4\times22\times17\times2$
= 2464 cm²

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Question 151 Mark

Find the surface area of a sphere of radius 5.6 cm.

Answer

r = 5.6 cm
Surface area of a sphere = $4\pi {r^2}$
$ = 4 \times \frac{{22}}{7} \times {(5.6)^2} = 394.24\;c{m^2}$

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Question 161 Mark

Find the surface area of a sphere of radius 10.5 cm.

Answer

r = 10.5 cm
Surface area of a sphere $=4\pi r^2$
= $4\times{22\over7}\times(10.5)^2$
= $4\times22\times10.5\times1.5$
= 1386 cm²

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Question 171 Mark

Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find total surface area of the cone.

Answer

Total surface area of cone = Curved surface Area of cone + Area of base
= $\pi rl$ + $\pi r$²
= [308 + $\frac { 22 } { 7 }$ $\times$ (7)²] cm²
= 462 cm²
Thus, the total surface area of the cone is 462 cm².

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Question 181 Mark

Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find the radius of the base

Answer

Slant height of cone = 14 cm
Let radius of circular end of cone be r.
Curved surface area of cone = $\pi rl$
308 cm² = ($\frac { 22 } { 7 }$ $\times$ r $\times$ 14) cm
$\Rightarrow$ r = $\left( \frac { 308 } { 44 } \right)$ cm = 7 cm
Thus, the radius of circular end of the cone is 7 cm.

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Question 191 Mark

The diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.

Answer

Diameter = 10.5 cm
$\Rightarrow$ Radius (r) =$\frac{10.5}{2}$= $\frac{21}{4}$ cm
Slant height of cone (l) = 10 cm
Now we have, Curved surface area of cone = $\pi rl$ = $\frac{22}{7}\times \frac{21}{4}\times 10$
= 165 cm²

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Question 201 Mark

The height and the slant height of a cone are 21 cm and 28 cm respectively. Find the volume of the cone.

Answer

We know that, l² = r² + h²,
Therefore , we have
$r=\sqrt{l^{2}-h^{2}}=\sqrt{28^{2}-21^{2}} \mathrm{cm}=7 \sqrt{7} \mathrm{cm}$
So, volume of the cone = $\frac{1}{3} \pi r^{2} h=\frac{1}{3} \times \frac{22}{7} \times 7 \sqrt{7} \times 7 \sqrt{7} \times 21 \mathrm{cm}^{3}$
= 7546 cm³

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Question 211 Mark

Find the surface area and total surface area of a hemisphere of radius 21 cm.

Answer

We know that the surface area S and total surfaces area S₁ of a hemisphere of radius r are given by
S = 2$\pi r ^ { 2 }$ and, S₁ = 3$\pi r ^ { 2 }$ respectively.
Here, r = 21 cm
$\therefore$ S = 2 $\times \frac { 22 } { 7 } \times$ 21 $\times$ 21 cm² and, S₁ = 3 $\times \frac { 22 } { 7 } \times$ 21 $\times$ 21 cm²
$\Rightarrow$ S = 2772 cm² and, S₁ = 4158 cm²

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Question 221 Mark

Find the surface area of a sphere of radius 7 cm.

Answer

We known that the surface area S of a sphere of radius r is given by
S = 4 $\pi r ^ { 2 }$
Here, r = 7 cm
$\therefore$ S = 4 $\times \frac { 22 } { 7 } \times$ 7 $\times$ 7 cm²= 616 cm²

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Question 231 Mark

A hemi spherical bowl has a radius of 3.5 cm. What would be the volume of water it would contain?

Answer

The volume of water the bowl contain = $\frac{2}{3}\pi {{r}^{3}}$
Radius = $3.5cm$
Then volume = $\frac{2}{3}\times \frac{22}{7}\times {{\left( 3.5 \right)}^{3}}$
$=\frac{2}{3}\times \frac{22}{7}\times 3.5\times 3.5\times 3.5$
$=\frac{2}{3}\times \frac{22}{7}\times \frac{35}{10}\times \frac{35}{10}\times \frac{35}{10}$
$=89.8c{{m}^{3}}$

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Question 241 Mark

Find the volume of a sphere of radius 11.2 cm.

Answer

We know that volume of sphere= $\frac 43 \pi r^3$
= $\frac 43 \times \frac {22}7 \times 11.2 \times 11.2 \times 11.2 cm^3$ = 5887.32 cm³

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Question 251 Mark

Find the curved surface area of a right circular cone whose slant height is 10 cm and base radius is 7 cm.

Answer

We know that,
Curved surface area of cone =$\pi r l$
$= \frac {22}7 \times 7 \times 10 cm^2$
$=$ 220 cm²

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