Tag: surface area of a prism and a pyramid

Questions Related to 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 

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 $

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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. $795 cm^3$

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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. $850 cm^3$

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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 $= 8 m$