Tag: surface area of cone

Quizzes (0) Questions (85)

Questions Related to surface area of cone

Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

What is the total surface area of a cone if its diameter =${ 1}$ ft and slant height = $12$ ft. (use $\displaystyle \pi =3.14$).

  1. $\displaystyle 11.625{ ft }^{ 2 }$
  2. $\displaystyle 18.625{ ft }^{ 2 }$
  3. $\displaystyle 19.625{ ft }^{ 2 }$
  4. $\displaystyle 19.625ft$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\displaystyle Diameter=\frac { radius }{ 2 } $
$\displaystyle radius=\dfrac{1}{2}ft$
Surface area of a cone $\displaystyle =\pi rs+\pi { r }^{ 2 }$
$\displaystyle 3.14\times { 1 }/{ 2 }\times 12+3.14\times { 1 }/{ 2 }\times { 1 }/{ 2 }$
$\displaystyle 18.84+0.785$
$\displaystyle 19.625{\  ft }^{ 2 }$

Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

An ice cream cone has radius of $21$ m and height of $20$ m. Find total surface area of the cone.

  1. $\displaystyle 3297{\ m }^{ 2 }$
  2. $\displaystyle 9734{ \ cm }^{ 2 }$
  3. $\displaystyle 3297\ mm$
  4. $\displaystyle 3297\ m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Find the value of slant height(s) of a ice-cream cone, using Pythagoras theorem, since the cross section is a right triangle.
$\displaystyle { s }^{ 2 }={ h }^{ 2 }+{ r }^{ 2 }$
$\displaystyle { s }^{ 2 }={ 20 }^{ 2 }+{ 21 }^{ 2 }$
$\displaystyle { s }^{ 2 }=400+441$
$\displaystyle s=\sqrt { 841 } $
$\displaystyle s=29$ m
So, surface area of a cone $\displaystyle =\pi rs+\pi { r }^{ 2 }$
$\displaystyle =3.14\times 21\times 29+3.14\times 21\times 21$
$\displaystyle =1912.26+1384.74$
$\displaystyle =3297{ m }^{ 2 }$

Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

What is the total surface area of a cone, if its radius = 5 cm and height = $\displaystyle\sqrt2 $cm?

  1. $\displaystyle 159.983{ \ mm }^{ 2 }$
  2. $\displaystyle 159.983{\ cm }^{ 2 }$
  3. $\displaystyle 159.983\ cm$
  4. $\displaystyle 159.983{ \ m }^{ 2 }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The value of slant height(s) of a cone, using Pythagoras theorem, since the cross section is a right triangle is

$s^2=h^2+r^2$
where 
h= height of cone
r=radius of the base of the cone
we know that
$h=\sqrt2\ cm$
$r=5\ cm$
$\therefore s^2=\sqrt2^2+5^2=2+25=27$
$\Rightarrow s^2=27$
$\Rightarrow s=\sqrt27$
$\Rightarrow s=5.19\ cm$

Total Surface area of cone$=\pi rs+\pi r^2$
$\pi=3.14$
$r=5\ cm$
$s=5.19\ cm$
$\therefore \pi rs+\pi r^2=3.14\times 5\times5.19+3.14\times 5\times5$
$=81.483+78.5$
$=159.983\ cm^2$

Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

The total surface area of a conical tent is $ 920$ square meter and its radius $14$ m. Find the slant height. (Round off your answer to the nearest whole number).

  1. $7$ m
  2. $6$ m
  3. $5$ m
  4. $6.5$ m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Formula:

Surface area of cone$=\pi rs+\pi r^2$
where r is the radius of the base of the cone and s is the slant height.
We know that surface area of cone$=940\ m^2$
$r =14\ m$
$\pi=3.14$
Substituting the values in the formula we get
$\Rightarrow 940=3.14 \times 1\times 4s+3.14\times 14^2$
$\Rightarrow 940=43.96\times s+3.14\times 196$
$\Rightarrow 940=43.96\times s+615.44$
$\Rightarrow 940-615.44=43.96\times s$
$\Rightarrow 324.56=43.96\times s$
$\Rightarrow s=\dfrac{324.56}{43.96}$
$\Rightarrow s=7.38\approx 7\ m$

Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

A closed cone tank radius $7$ cm and height $10$ cm is made from a sheet of aluminium. How much sheet is required?

  1. $144cm^2$
  2. $\displaystyle 22\sqrt { 149 } cm^2$
  3. $\displaystyle (22\sqrt { 149 } +144) cm^2$

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total surface area of cone  = Area of base + Area of curved surface
$\displaystyle =\quad \pi { r }^{ 2 }+\pi rs$

$\displaystyle =\frac { 22 }{ 7 } \times 7\times 7+\frac { 22 }{ 7 } \times 7\left( \sqrt { 149 }  \right) $
$\displaystyle s=\sqrt { { h }^{ 2 }+{ r }^{ 2 } } $
$\displaystyle =\sqrt { 149+100 } $
$\displaystyle =144+22\sqrt { 149 } $

Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

Find  the radius of the base of a right circular cone which has a lateral surface area of $6\pi$ and a slant height of $6$ ( in standard units )

  1. $0.50$
  2. $0.75$
  3. $1.00$
  4. $1.25$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, Lateral surface area $=6 \pi$ and slant height $=6$

Let the radius of base be $r$ and slant height of cone be $l = 6$.
Lateral surface area is equal to $\pi rl = \pi \times r \times 6 = 6\pi$
$\Rightarrow 6 \pi= \pi \times r \times 6$
$\Rightarrow r=1$

Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

Find the slant height and vertical height of a Cone with radius $5.6$ cm and curved surface area $158.4$ cm$^2$.

  1. $8.07$
  2. $7.05$
  3. $8$

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Radius $=5.6$ cm, vertical height $= h$, slant height $=$ $l$
Curved Surface Area of cone $=\pi r l = 158.4 cm^2$
$\Rightarrow \dfrac{22}{7} \times 5.6 \times l = 158.4$
$\Rightarrow l = \dfrac{158.4 \times 7}{22 \times 5.6} = \dfrac{18}{2} = 9$ cm
We know $l^2 = r^2 + h^2$
Thus $h^2 = l^2 - r^2 $

$= 9^2 - (5.6)^2$
$= 81 - 31.36$
$= 49.64$
$h = \sqrt{49.64}$
$h = 7.05 $ cm (approx.)

Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

The curved surface area of right circular cone with height $24$ m and radius $7$ m is

  1. $500\ \text{m}^{2}$
  2. $550\ \text{m}^{ 2 }$
  3. $607\ \text{m}^{ 2 }$
  4. $650\ \text{m}^{ 2 }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Height of cone$=24m$
Radius of cone$=7m$
Slant height of cone$=\sqrt { { 24 }^{ 2 }+{ 7 }^{ 2 } } =\sqrt { 576+49 } =\sqrt { 625 } =25m$
CSA of cone$=\pi rl=\cfrac { 22 }{ 7 } \times 7\times 25=550 m^2$