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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}

Similar Questions :

1. 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

2. A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m cube) is:

  • 4120 m cube
  • 4140 m cube
  • 5140 m cube
  • 5120 m cube

Answer: Option D

Explanation:

l = (48 - 16)m = 32 m, [because 8+8 = 16]
b = (36 -16)m = 20 m,
h = 8 m.

Volume of the box = (32 x 20 x 8) m cube
= 5120 m cube.

3. How many cubes of 10 cm edge can be put in a cubical box of 1 m edge.

  • 10000 cubes
  • 1000 cubes
  • 100 cubes
  • 50 cubes

Answer: Option B

Explanation:

\begin{aligned}
\text{Number of cubes =}\frac{100*100*100}{10*10*10} \\
= 1000
\end{aligned}

Note: 1 m = 100 cm

4. The maximum length of a pencil that can he kept is a rectangular box of dimensions 8 cm x 6 cm x 2 cm, is

  • \begin{aligned} 2\sqrt{17} \end{aligned}
  • \begin{aligned} 2\sqrt{16} \end{aligned}
  • \begin{aligned} 2\sqrt{26} \end{aligned}
  • \begin{aligned} 2\sqrt{24} \end{aligned}

Answer: Option C

Explanation:

In this question we need to calculate the diagonal of cuboid,
which is =
\begin{aligned}
\sqrt{l^2+b^2+h^2} \\
= \sqrt{8^2+6^2+2^2} \\
= \sqrt{104} \\
= 2\sqrt{26}
\end{aligned}

5. 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

Read more from - Volume and Surface Area Questions Answers
Post a comment

  • Cannon 11 years ago

    A spilme and intelligent point, well made. Thanks!

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