Tag: maths

Questions Related to maths

The base of right prism is a triangle whose perimeter is 28 cm and the inradius of the triangle is 4 cm. If the volume of the prism is 366 cc, then its height is 

maths measures and the circle surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

  1. 6.54 cm

  2. 8 cm

  3. 4 cm

  4. None of these

Show answer
Correct Option: A
Explanation:

Perimeter of triangle is $2{s}=28\ cm\implies s=14$

Inradius of triangle $r=4\implies \Delta=r.s=56$
Volume of prism $=366$ cc
$\implies $ Area of triangle $\times $ height $=366$
Height $=\dfrac{366}{56}=6.54$

For a prism, $A = 60^o$, $\mu = \sqrt{\dfrac{7}{3}}$, then the minimum possible angle of incidence, so that the light ray is refracted from the second surface is

maths measures and the circle surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

  1. $30^o$

  2. $60^o$

  3. $90^o$

  4. $40^o$

Show answer
Correct Option: A

The slant height of a right pyramid having square base of side $10cm$ and vertical height $15cm$ is

maths measures and the circle surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

  1. $5\sqrt{10}cm$

  2. $6\sqrt{10}cm$

  3. $7\sqrt{10}cm$

  4. $8\sqrt{10}cm$

Show answer
Correct Option: A

Consider an incomplete pyramid of balls on a square base having $18$ players, and having $13$ balls on each side of the top layer. Then the total number $N$ of balls in that pyramid satisfies 

maths measures and the circle surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

  1. $ 9000 < N <10000$

  2. $8000 < N < 9000$

  3. $7000 < N < 8000$

  4. $ 10000 < N < 12000 $

Show answer
Correct Option: B
Explanation:

Top layer has $(13 \times 13)$ balls 
Similarly one layer below top layer will have $(14 \times 14) $ balls and we have $18$ lesens to total number of ball 
$ N = (13)^2 + (14)^2 + . . . . + (30)^2 $

$\displaystyle N = \frac {30 \times 31 \times 61} {6} = \frac {12 \times 13 \times 25} {6}$

$ N = 8805 $

The circumference of a 1 cm thick pipe is 44 cm. The level of water that 7 cm of pipe can hold is

maths measures and the circle surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

  1. $798 cm^3$

  2. $308 cm^3$

  3. $792 cm^3$

  4. $795 cm^3$

Show answer
Correct Option: C
Explanation:

Given that

$2\pi r=44$
$r=7\ cm$

So, the inner radius of the pipe $=7-1=6\ cm$

Therefore, the volume of the pipe
$=\pi r^2h$
$=\pi \times 6^2\times 7$
$=792\ cm^3$

Hence, this is the answer.

The base of a right prism is a square of perimeter 20 cm and its height is 30 cm. The volume of the prism is

maths measures and the circle surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

  1. $700 cm^3$

  2. $750 cm^3$

  3. $800 cm^3$

  4. $850 cm^3$

Show answer
Correct Option: B
Explanation:

Given, perimeter $=4a=20$cm
$\therefore a=5$ cm
Area $=a^2=25  cm^2$
Volume $=$ Area $\times$ Height
Volume $=25 \times 30$
Volume $=750  cm^3$

The base of a right prism is an equilateral triangle of edge $12$m. If the volume of the prism is $288\sqrt 3m^3$, then its height is:

maths measures and the circle surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

  1. $6$m

  2. $8$m

  3. $10$m

  4. $12$m

Show answer
Correct Option: B
Explanation:

length of Equilateral triangle $= 12 m$
Area of equilateral triangle = $\displaystyle \frac{\sqrt{3}}{4}a^2$ = $\displaystyle \frac{\sqrt{3}}{4}(12)^2$ = $36\sqrt{3}$
Volume of prism = $288\sqrt{3} m^3$ = Area of triangle X height
$288\sqrt{3} m^3$ = $36 \sqrt{3} \times$ height
$\therefore $ Height $= 8 m$

In any triangle, the side opposite to the larger (greater) angle is longer

maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

A greater angle of a angle is opposite a greater side$.$ Let $ABC$ be a triangle in which angle $ABC$ is greater than angle $BCA;$ then side $AC$ is also greater than side $AB.$ For if it is no greater$,$ then $AC$ is either equal to $AB$ or less$.$

Hence$,$ option $(A)$ is always true$.$

For a triangle $ABC$, the true statement is:

maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

  1. ${ AC }^{ 2 }={ AB }^{ 2 }+{ BC }^{ 2 }$

  2. $AC=AB+BC$

  3. $AC>AB+BC$

  4. $AC<\,AB+BC$

Show answer
Correct Option: D
Explanation:

For any $\triangle ABC$, sum of two sides must be greater than the third side.
Hence, $AB + BC > AC$.

Two sides of a triangle are of lengths 5 cm and 1.5 cm, then the length of the third side of the triangle cannot be

maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

  1. $\displaystyle3.6\,cm$

  2. $\displaystyle4.1\, cm$

  3. $\displaystyle3.8\, cm$

  4. $\displaystyle3.4\, cm$

Show answer
Correct Option: D
Explanation:

In a triangle, the difference between two sides should be less than the third side.
Hence,option D is correct $3.4\ cm$