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A cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm. The percentage of the wood wasted is :

  • 45%
  • 56%
  • 67%
  • 75%

Answer: Option D

Explanation:

We will first subtract the cone volume from wood volume to get the wood wasted.
Then we can calculate its percentage.

\begin{aligned}
\text{Sphere Volume =}\frac{4}{3}\pi r^3 \\
\text{Cone Volume =}\frac{1}{3}\pi r^2h\\

\text{Volume of wood wasted =}\\
\left(\frac{4}{3}\pi *9*9*9\right)-\left(\frac{1}{3}\pi *9*9*9\right) \\
= \pi *9*9*9 cm^3 \\
\text{Required Percentage =} \\
\frac{\pi *9*9*9}{\frac{4}{3}\pi *9*9*9}*100 \% \\
= \frac{3}{4}*100 \% \\
= 75\%
\end{aligned}

Similar Questions :

1. If a right circular cone of height 24 cm has a volume of 1232 cm cube, then the area of its curved surface is :

  • \begin{aligned} 450 cm^2 \end{aligned}
  • \begin{aligned} 550 cm^2 \end{aligned}
  • \begin{aligned} 650 cm^2 \end{aligned}
  • \begin{aligned} 750 cm^2 \end{aligned}

Answer: Option B

Explanation:

Volume is given, we can calculate the radius from it, then by calculating slant height, we can get curved surface area.
\begin{aligned}
\frac{1}{3}*\pi *r^2*h = 1232 \\
\frac{1}{3}*\frac{22}{7}*r^2*24 = 1232 \\
r^2 = \frac{1232*7*3}{22*24} = 49 \\
r = 7 \\
\text{Now, r = 7cm and h = 24 cm } \\
l = \sqrt{r^2+h^2} \\
= \sqrt{7^2+24^2} = 25cm \\
\text{Curved surface area =}\pi rl\\
= \frac{22}{7}*7*25 = 550 cm^2
\end{aligned}

2. Find the surface area of a 10cm*4cm*3cm brick.

  • 154 cm square
  • 156 cm square
  • 160 cm square
  • 164 cm square

Answer: Option D

Explanation:

Surface area of a cuboid = 2(lb+bh+hl) cm square
So,
Surface area of a brick = 2(10*4+4*3+3*10) cm square
= 2(82) cm square = 164 cm square

3. A cistern 6 m long and 4 m wide contains water up to a breadth of 1 m 25 cm. Find the total area of the wet surface.

  • 42 m sqaure
  • 49 m sqaure
  • 52 m sqaure
  • 64 m sqaure

Answer: Option B

Explanation:

Area of the wet surface =
2[lb+bh+hl] - lb = 2 [bh+hl] + lb
= 2[(4*1.25+6*1.25)]+6*4 = 49 m square

4. How many bricks, each measuring 25cm*11.25cm*6cm, will be needed to build a wall 8m*6m*22.5m

  • 6100
  • 6200
  • 6300
  • 6400

Answer: Option D

Explanation:

To solve this type of question, simply divide the volume of wall with the volume of brick to get the numbers of required bricks
So lets solve this

Number of bricks =
\begin{aligned}
\frac{\text{Volume of wall}}{\text{Volume of 1 brick}} \\
= \frac{800*600*22.5}{25*11.25*6} \\
= 6400
\end{aligned}

5. 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length if the wire in meters will be:

  • 76 m
  • 80 m
  • 84 m
  • 88 m

Answer: Option C

Explanation:

Let the length of the wire be h
\begin{aligned}
Radius = \frac{1}{2}mm = \frac{1}{20}cm\\
\pi r^2h = 66 \\
\frac{22}{7}*\frac{1}{20}*\frac{1}{20}*h = 66 \\
=> h = \frac{66*20*20*7}{22} \\
= 8400 cm \\
= 84 m
\end{aligned}

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