Tag: surface area of a prism and a pyramid

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Questions Related to surface area of a prism and a pyramid

Multiple choice maths surface area and volume of sphere solids surface area of a prism surface area of a prism and a pyramid volume of a sphere surface areas and volumes of solids problems involving volume of combined solids application of surface area and volume of solids

From a solid sphere of radius $R$, a concentric solid sphere of radius $\dfrac{R}{2}$ is removed. The total surface area increases by

  1. $0\%$
  2. $25\%$
  3. $50\%$
  4. $75\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Solution:- (B) $25 \%$
Initial area of sphere $ \left( {A} _{1} \right) = 4 \pi {R}^{2}$
New area of sphere $\left( {A} _{2} \right) = 4 \pi {R}^{2} + 4 \pi {\left( \cfrac{R}{2} \right)}^{2} = 5 \pi {R}^{2}$
$\therefore$ Increase in area $= \cfrac{{A} _{2} - {A} _{1}}{{A} _{1}} \times 100$
$\Rightarrow$ Increase in area $= \cfrac{5 \pi {R}^{2} - 4 \pi {R}^{2}}{4 \pi {R}^{2}} \times 100 = 25 \%$
Hence the area will be increased by $25 \%$.
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 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).