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The volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is:

  • \begin{aligned} 79.8 cm^3 \end{aligned}
  • \begin{aligned} 79.4 cm^3 \end{aligned}
  • \begin{aligned} 89.8 cm^3 \end{aligned}
  • \begin{aligned} 89.4 cm^3 \end{aligned}

Answer: Option C

Explanation:

Volume of the largest cone = Volume of the cone with diameter of base 7 and height 7 cm

\begin{aligned}
\text{Volume of cone =}\frac{1}{3}\pi r^2h \\
= \frac{1}{3}*\frac{22}{7}*3.5*3.5*7 \\
= \frac{269.5}{3}cm^3 \\
= 89.8 cm^3
\end{aligned}

Note: radius is taken as 3.5, as diameter is 7 cm

Similar Questions :

1. A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets into it. The mass of the man is :

  • 50 kg
  • 60 kg
  • 70 kg
  • 80 kg

Answer: Option B

Explanation:

In this type of question, first we will calculate the volume of water displaces then will multiply with the density of water.
Volume of water displaced = 3*2*0.01 = 0.06 m cube

Mass of Man = Volume of water displaced * Density of water

= 0.06 * 1000 = 60 kg

2. 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}

3. 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

4. The radii of two cones are in ratio 2:1, their volumes are equal. Find the ratio of their heights.

  • 1:4
  • 1:3
  • 1:2
  • 1:5

Answer: Option A

Explanation:

Let their radii be 2x, x and their heights be h and H resp.
Then,
\begin{aligned}
\text{Volume of cone =}\frac{1}{3}\pi r^2h \\
\frac{\frac{1}{3}*\pi *{(2x)}^2*h}{\frac{1}{3}*\pi *{x}^2*H} \\
=> \frac{h}{H} = \frac{1}{4} \\
=> h:H = 1:4
\end{aligned}

5. The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km square. The height of mountain is :

  • 2.3 km
  • 2.4 km
  • 2.5 km
  • 2.6 km

Answer: Option B

Explanation:

Let the radius of the base be r km. Then,
\begin{aligned}
\pi r^2 = 1.54 \\
r^2 = \frac{1.54*7}{22} = 0.49\\
= 0.7 km \\
\text{Now l=2.5 km, r = 0.7 km} \\
h = \sqrt{2.5^2 - 0.7^2} km \\
=\sqrt{6.25 - 0.49}\\
=\sqrt{5.76} km \\
= 2.4 km
\end{aligned}

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