Tag: measures and the circle

Quizzes (3) Questions (9)

Questions Related to measures and the circle

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

State whether true or false : 

If $s$ is the perimeter of the base of a prism, $n$ is the number of sides of the base, $S$ is the total length of the edges and $h$ is the height, then $S=nh+2s$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

True. Total length of Prism $= S$
Length of all the heights $= nh$
Perimeter of base and head $= 2s$
$\therefore S = nh + 2s$

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

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 

  1. 6.54 cm

  2. 8 cm

  3. 4 cm

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $=\dfrac{366}{56}=6.54$

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

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

  1. $30^o$
  2. $60^o$
  3. $90^o$
  4. $40^o$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a prism, the condition for refraction at the second surface is that the angle of incidence at the second surface must be less than the critical angle. Using Snell's law and the prism relation r1 + r2 = A, the minimum angle of incidence is found by setting r2 equal to the critical angle.

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

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

  1. $5\sqrt{10}cm$
  2. $6\sqrt{10}cm$
  3. $7\sqrt{10}cm$
  4. $8\sqrt{10}cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a right square pyramid, the slant height s is the hypotenuse of a right triangle formed by the vertical height h and half the base side length a/2. Thus, s = sqrt(h^2 + (a/2)^2) = sqrt(15^2 + 5^2) = sqrt(225 + 25) = sqrt(250) = 5*sqrt(10).

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

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 

  1. $ 9000 < N <10000$
  2. $8000 < N < 9000$
  3. $7000 < N < 8000$
  4. $ 10000 < N < 12000 $
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $

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

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

  1. $798 cm^3$
  2. $308 cm^3$
  3. $792 cm^3$
  4. $795 cm^3$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. $700 cm^3$
  2. $750 cm^3$
  3. $800 cm^3$
  4. $850 cm^3$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $=750  cm^3$

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

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:

  1. $6$m
  2. $8$m
  3. $10$m
  4. $12$m
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $= 8 m$