2 Marks Questions

Question 12 Marks

The volume of a right circular cone is $9856 \mathrm{~cm}^3$. If the diameter of the base is $28 \ cm$ , Find: Slant height of the cone.

Answer

It is given that: Radius of the cone $(\mathrm{r})=14 \mathrm{~cm}$ Height of the cone $=48 \mathrm{~cm}$ Slant height $(\mathrm{l})=$ ? Now we know that
$\mathrm{l}=\sqrt{\mathrm{r}^2+\mathrm{h}^2}$
$\mathrm{l}=\sqrt{14^2+48^2}$
$=\sqrt{2500}$
$=50 \mathrm{~cm}$
Therefore the slant height of the cone is 5$0 \ cm .$

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Question 22 Marks

The volume of a right circular cone is $9856\ cm^2$. If the diameter of the base is $28\ cm$, Find: Height of the cone.

Answer

It is given that diameter of the cone $(d) = 28cm$
Radius of the cone (r) $=\frac{\text{d}}{2}$
$=\frac{28}{2}=14\text{cm}$ Height of the cone $= ?$
Now, Volume of the cone (v) $=\frac{1}{3}\pi\text{r}^2\text{h}=9856\text{cm}^3$
$\Rightarrow\frac{1}{3}\times3.14\times14^2\times\text{h}=9856$
$\Rightarrow\text{h}=\frac{9856\times3}{3.14\times14\times14}=48\text{cm}$
Therefore the height of the cone is $48\ cm.$

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Question 32 Marks

Find the volume of the right circular cone with the following dimensions: Radius $6\ cm$, height $7\ cm.$

Answer

It is given that: Radius of the cone $(r) = 6\ cm$
Height of the cone $(h) = 7\ cm$
Volume of a right circular cone$=\frac{1}{3}\pi\text{r}^2\text{h}$
$=\frac{1}{3}\times3.14\times6^2\times7=264\text{cm}^3$

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Question 42 Marks

Find the curved surface area of a cone, if its slant height is $60\ cm$ and the radius of its base is $21\ cm.$

Answer

It is given that:
Slant height of cone $(l)=60 \mathrm{~cm}$
Radius of the base of the cone( $r$ $)=21 \mathrm{~cm}$
Curved Surface Area $(C.S.A) = ?$
$C.S.A =\pi \mathrm{rl}=\frac{22}{7 \times 21} \times 60=3960 \mathrm{~cm}^2$
Therefore the curved surface area of the right circular cone is $3960 \mathrm{~cm}^2$

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Question 52 Marks

The volume of a right circular cone is 9856cm$^3$. If the diameter of the base is $28\ cm$, Find: Curved surface area of the cone.

Answer

Radius of the cone $(r)=14 cm$ Slant height of the cone $(I)=50 cm$
Curved surface area $(C . S . A)=$ ?
Curved surface area of a cone $(C . S . A)=\pi r l=3.14 \times 14 \times 50=2200 cm^2$
Therefore curved surface of the cone is $2200 cm^3$.

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Question 62 Marks

Find the volume of the right circular cone with the following dimensions: Height is $21\ cm$ and slant height is $28\ cm.$

Answer

It is given that: Height of the cone $(h) = 28\ cm$ Slant height of the cone $(l) = 21\ cm$ As we know that,$\text{l}^2=\text{r}^2+\text{h}^2$
$\text{r}=\sqrt{\text{l}^2-\text{h}^2}$
$\text{r}=\sqrt{\text{28}^2-\text{21}^2}$
Volume of a right circular cone:$=\frac{1}3{}\pi\text{r}^2\text{h}$
$=\frac{1}{3}\times3.14\times\big(7\sqrt{7}\big)^2\times18$
$=7546\text{cm}^3$

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Question 72 Marks

Find the volume of the right circular cone with the following dimensions: Radius is $3.5\ cm$, height is $12\ cm.$

Answer

It is given that: Radius of the cone $(r) = 3.5\ cm$
Height of the cone $(h) = 12\ cm$
Volume of a right circular cone$=\frac{1}{3}\pi\text{r}^2\text{h}$
$=\frac{1}{3}\times3.14\times3.5^2\times12$
$=154\text{cm}^3$

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Question 82 Marks

Find the curved surface area of a cone with base radius $5.25\ cm$ and slant height $10\ cm.$

Answer

It is given that:
Base radius of the cone $(r)=5.25 \mathrm{~cm}$
Slant height of the cone $(I)=10 \mathrm{~cm}$
Curved Surface Area (C.S.A) $=\pi \mathrm{rl}$
$=\frac{22}{7} \times 5.25 \times 10=165 \mathrm{~cm}^2$
Therefore the curved surface area of the cone is $165 \mathrm{~cm}^2$

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