Tag: perimeter, area and volume

Quizzes (18) Questions (27)

Questions Related to perimeter, area and volume

Multiple choice maths perimeter, area and volume surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

If a regular square pyramid has a base of side $8 cm$ and height of $30 cm$, then its volume is

  1. $120 cm^3.$
  2. $240 cm^3.$
  3. $640 cm^3.$
  4. $900 cm^3.$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given that:
Side $a=8\ cm$, Height $h=30\ cm$
As we know that
Volume of regular square pyramid 
$\Rightarrow a^2\dfrac{h}{3}$
$\Rightarrow 8^2\dfrac{30}{3}$
$\Rightarrow 64\times 10$
$\Rightarrow 640\ cm^3$
This is the required solution.
Multiple choice maths perimeter, area and volume surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

A square pyramid can contain $16\ m^3$ of water. The height of the pyramid is $3\ m$. Calculate the length of base of the square pyramid.

  1. $16\ m$
  2. $12\ m$
  3. $4\ m$
  4. $2\ m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of square pyramid  $=16{ m }^{ 3 }$

$\Rightarrow \quad \dfrac { 1 }{ 3 } \times { a }^{ 2 }\times h=16{ m }^{ 3 }\Rightarrow \dfrac { 1 }{ 3 } \times { a }^{ 2 }\times 3=16\Rightarrow a=\sqrt { 16 } =4cm$
$\therefore $  Length of base $= 4m$

Multiple choice maths perimeter, area and volume surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

$VPQRS$ is rectangle based pyramid where $PQ = 30\ cm, QR = 20\ cm$ and volume is $2000\ {cm}^3$, then height (in cm) is

  1. $20$
  2. $40$
  3. $10$
  4. $30$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given : Length of base$(l)=30\ cm$, width of base$(h)=20\ cm$, Volume of pyramid$=2000\ cm^3$

Let $h$ be the height of the pyramid
We know that, volume of pyramid $=\dfrac{l\times w\times h}{3}$
$\implies 2000\ cm^3 = \dfrac{30 cm\times 20 cm\times h}{3}$
$\implies h=\dfrac{2000\times 3}{30\times 20} cm=10 cm$
Hence, height is $10 cm$.

Multiple choice maths perimeter, area and volume volume of prism and pyramid surface areas and volumes of solids recall the surface areas and volumes of different solid shapes

A frustum of a pyramid has an upper base $100\ m$ by $10\ m$ and a lower base of $80\ m$ by $8\ m$. if the altitude of the frustum is $5\ m$, find its volume (in cu. m).

  1. $4567.67$
  2. $3873.33$
  3. $4066.67$
  4. $2345.98$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Give : Height of pyramid$(h)=5\ m$ 

It is a pyramid with rectangular base.
Edge of upper base $length(L)=100\ m, breadth(B)=10\ m$

Edge of lower base $length(l)=80\ m, breadth(b)=8\ m$
Area of upper base$(A _{1})=L\times B=100\times 10 = 1000\ m^2$
Area of lower base$A _{2}=l\times b=640\ m^2$
Volume of frustum$(V)=\dfrac{h}{3}(A _{1} + A _2 + \sqrt{A _1 \times A _2})$
$\implies$$(V)=\dfrac{5}{3}(1000 + 640 + \sqrt{1000 \times 640})$
                 $=\dfrac{5}{3}(1640+800)=\dfrac{5}{3}(2440)=4066.666667$
Hence, volume$(V)=4066.67\ cu. m$

Multiple choice maths perimeter, area and volume volume of prism and pyramid surface areas and volumes of solids recall the surface areas and volumes of different solid shapes

A regular triangular pyramid has an altitude of $9\ m$ and a volume of $187.06\ cu.\ m$. What is the base edge in meters?

  1. $12$
  2. $13$
  3. $14$
  4. $15$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given : Altitude$(height\quad (h))=9\ m$, volume $=187.06\ cu.\ m$

We know that, Volume $=\dfrac{1}{3}Bh$, where $B=x^2 \sin \theta$
$\implies 187.06=\dfrac{1}{3} \left(\dfrac{1}{2}x^2 (\sin \theta)\right) (9)$,  where $x$ is base edge
$\implies 187.06=\dfrac{1}{3} \left(\dfrac{1}{2}x^2 \sin60\right)9$
$\implies x^2=143.9988=144$
$\therefore\ x=12\ m$

Multiple choice maths perimeter, area and volume volume of prism and pyramid surface areas and volumes of solids recall the surface areas and volumes of different solid shapes

The frustum of a regular triangular pyramid has equilateral triangles for its bases. The lower and upper base edges are $9\ m$ and $3\ m$, respectively. If the volume is $118.2\ cu.\ m$, how far apart (m) are the base?

  1. $9$
  2. $8$
  3. $7$
  4. $10$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given : Volume $=118.2\ cu. m$

Upper base edge $=9\ m$, lower base edge $=3\ m$
We know that, 
Volume $=\dfrac{h}{3}(A _{1}+A _{2}+\sqrt{A _{1} A _{2}})$ ....... $(1)$, where $A _{1}, A _{2}$ are area of upper and lower bases.
$A _{1}=\dfrac{\sqrt{3}}{4}\times 9^2=35.074$
$A _{2}=\dfrac{\sqrt{3}}{4}\times 3^2=3.897$
From $(1)$ we get,
$118.2 = \dfrac{h}{3}(35.074+3.897+\sqrt{35.074\times 3.897})$
$\implies 118.2=\dfrac{h}{3}(38.971+11.6911)$
$\implies 118.2\times 3=h(50.6621)$
$\implies h=7\ m$
Hence, the bases are $7\ m$ far from each other.

Multiple choice maths perimeter, area and volume volume of prism and pyramid surface areas and volumes of solids recall the surface areas and volumes of different solid shapes

A regular hexagonal pyramid whose base perimeter is $60\ cm$ has an altitude of $30\ cm$, the volume of the pyramid (in cu. cm)is:

  1. $2958$
  2. $2598$
  3. $2859$
  4. $2589$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given : Perimeter of regular hexagon $=60\ cm$ and height $=30\ cm$

We know that, regular hexagon has all its sides of equal length
$\therefore$ Perimeter $=6a=60\ cm$,  where $a$ is side of hexagon
$\implies a=10\ cm$
There are exactly $6$ equilateral triangle
Area of one equilateral triangle $=\dfrac{\sqrt{3}}{4}a^2$
                                                     $=\dfrac{\sqrt{3}}{4}\times 10^2=25\sqrt{3}$
$\therefore$ Area of $6$ equilateral triangles $=6\times 25\sqrt{3}=150\sqrt{3}$
$\therefore\ Area\ of\ base = 150\sqrt{3}$
Volume $=\dfrac{1}{3}\times base \times height$
              $=\dfrac{1}{3}\times 150\sqrt{3}\times 30$
              $=1500\sqrt{3}=2598\ cu. m$
Hence, volume of pyramid is $2598\ cu. m$.

Multiple choice maths perimeter, area and volume volume of prism and pyramid surface areas and volumes of solids recall the surface areas and volumes of different solid shapes

A pyramid whose base is a regular pentagon of area $42\ {cm}^2$ and whose height is $7$ cm. What is the volume (in ${cm}^3$) of the pyramid?

  1. $98$
  2. $105$
  3. $126$
  4. $147$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given : Area of base of pyramid $=42\ cm^2$, height $=7\ cm$

We know that, Volume of pyramid $=\dfrac{1}{3}\times Area\ of\ base \times height$
                                                          $=\dfrac{1}{3}\times 42\times 7$
                                                          $=98\ cm^3$
Hence, volume of pyramid is $98\ cm^3$.