Tag: maths

Questions Related to maths

The curved surface area of right circular cone with height $24$ m and radius $7$ m is

maths solids surface area of a cone surface area of cone the surface area of a cone

  1. $500\ \text{m}^{2}$

  2. $550\ \text{m}^{ 2 }$

  3. $607\ \text{m}^{ 2 }$

  4. $650\ \text{m}^{ 2 }$

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Correct Option: B
Explanation:
Height of cone$=24m$
Radius of cone$=7m$
Slant height of cone$=\sqrt { { 24 }^{ 2 }+{ 7 }^{ 2 } } =\sqrt { 576+49 } =\sqrt { 625 } =25m$
CSA of cone$=\pi rl=\cfrac { 22 }{ 7 } \times 7\times 25=550 m^2$

A cone and a cylinder have the same base area. They also have the same curved surface area. If the height of the cylinder is $3$ m, then the slant height of the cone (in m) is

maths solids surface area of a cone surface area of cone the surface area of a cone

  1. $3$

  2. $4$

  3. $6$

  4. $7$

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Correct Option: C
Explanation:

Given the radius of cylinder and cone are the same because there base areas are same.
Curved surface of cylinder $=$ curved surface area of the cone
$\therefore 2 \pi r h = \pi r l$
$\therefore l = 2h $
Given, height of cylinder $= 3$ cm
Therefore, slant height of cone $= 6$ cm

The curved surface area of a right circular cone with height $24$ cm and radius $7$ cm is

maths solids surface area of a cone surface area of cone the surface area of a cone

  1. $500 cm^2$

  2. $550 cm^2$

  3. $607 cm^2$

  4. $650 cm^2$

Show answer
Correct Option: B
Explanation:

Given,
Radius of cone $= 7$ cm
Height of cone $= 24$ cm
Curved surface area = $\pi r \sqrt{(r^2 + l^2)}$
= $\pi \times 7 (\sqrt{(7^2 + (24)^2)}$
= $\pi \times 70\times 25$
= $550 cm^2$

Consider two cones, the curved surface area of one being twice that of the other and the slant height of the later being twice that of the former. The ratio of the radius of the later cone to that of the former is

maths solids surface area of a cone surface area of cone the surface area of a cone

  1. $1 : 4$

  2. $1 : 2$

  3. $2 : 1$

  4. $4 : 1$

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Correct Option: A
Explanation:

Let the curved surface areas of two cones be $C _1$ and $C _2$

And their slant heights be $l _1$ and $l _2$
Given, $C _1=2C _2$
$l _2=2l _1$

$\therefore \pi r _1l _1=2\pi r _2.2l _1$
$\therefore r _1=4r _2$

The curved surface area of a right cone is $\displaystyle 286 m^{2}$ and its the slant height is 13 m, then volume is

maths solids surface area of a cone surface area of cone the surface area of a cone

  1. $\displaystyle 821.389m^{3}$

  2. $\displaystyle 852.258m^{3}$

  3. $\displaystyle 364.369m^{3}$

  4. $\displaystyle 281.164m^{3}$

Show answer
Correct Option: D
Explanation:

Curved surface area of a cone $= \pi rl$  where r is
the radius of the cone and l is the slant height.
Hence, CSA of this cone, $ = \frac {22}{7} \times r \times 13 = 286 $
$ => r = 7  m $

For a cone, l $ = \sqrt { { h }^{ 2 }+  {r}^{ 2 } } $ where lis the slant height.

Hence, $ 13 = \sqrt { { h }^{ 2 }+  {7}^{ 2 } } $ 

$ 169 = { h }^{ 2 } + 49 $

$ { h }^{ 2 } = 120 $

$ h = 2 \sqrt {30}  m $

Hence, volume of this cone $ = \frac { 1 }{ 3 } \times \frac { 22 }{ 7 } \times { 7 }^{ 2 }\times 2 \sqrt {30} = \frac {154}{3} \sqrt {30} { m }^{ 3 } $


The cost of the canvas required to make a conical tent of base radius $8$ m at the rate of Rs. $40$ per $\displaystyle m^{2}$ is Rs. $10,048$. Find the height of the tent .$\displaystyle \left ( Take\  \pi =3.14 \right )$ 

maths solids surface area of a cone surface area of cone the surface area of a cone

  1. $6$ m

  2. $7$ m

  3. $8$ m

  4. $10$ m

Show answer
Correct Option: A
Explanation:

To find the amount of canvas required to make a conical tent, we need to calculate the lateral surface area of the tent.
Lateral surface area of a cone of radius $ r $, height $ h = \pi r\sqrt{{h}^{2} + {r}^{2}} $
As the total cost to make the tent is Rs $10048 $ at the rate of Rs $ 40 $ per sq m, total area LSA $ = \dfrac {10048}{40} = 251.2 $ sq m 

So, $ \pi r \times \sqrt{{h}^{2} + {r}^{2}} = 251.2 $
$ \Rightarrow  3.14 \times 8 \times \sqrt{{h}^{2} + {8}^{2}} = 251.2 $
$ \Rightarrow  \sqrt{{h}^{2} + {8}^{2}} = 10 $
$ \Rightarrow  {h}^{2} + 64 = 100 $
$ \Rightarrow  {h}^{2}  = 36 $
$ \Rightarrow  h = 6 $ m 

The rate of $GST$ on stainless steel is $18\% $ of which the share of a state government is

maths gst (goods and service tax) more about gst commission, brokerage and vat taxation, calculation of income tax

  1. $18\%$

  2. $9\%$

  3. $36\%$

  4. None of these

Show answer
Correct Option: B
Explanation:
rate of GST $= 18 \%$

Rate of CGST $=$ Rate Of SGST

rate of CGST + rate of SGST $= 18 \%$

$2\times $ rate of SGST $= 18 \%$

rate of SGST $= 9 \%$

state gov. share will be$ 9 \%$

The rate of GST on stainless steel utensils is $18$%, then the rate of State GST is

maths gst (goods and service tax) more about gst commission, brokerage and vat taxation, calculation of income tax

  1. $18$%

  2. $9$%

  3. $36$%

  4. $0.9$%

Show answer
Correct Option: B
Explanation:

If GST is 18%, State GST or SGST is 9% and CGST is 9%.

Shop Inspection as part of a Registration in GST will be:

maths gst (goods and service tax) more about gst commission, brokerage and vat taxation, calculation of income tax

  1. A Pre-Condition for giving approval for a Registration Application

  2. Shop Inspection after the issuance of the GSTIN in all cases

  3. Only at the business place of those dealers which comes under the Risk Parameters of the concerned GST Officials or Risk Profile given by GSTN Common Portal

  4. No Shop Inspection at all

Show answer
Correct Option: C

Rate of GST on brokerage is .....

maths gst (goods and service tax) more about gst commission, brokerage and vat taxation, calculation of income tax

  1. $5$%

  2. $12$%

  3. $18$%

  4. $28$%

Show answer
Correct Option: C
Explanation:

Rate of GST on brokerage is $18$%.