Question Detail

A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surface will be :

\begin{aligned} 2:1 \end{aligned}
\begin{aligned} 1:\sqrt{2} \end{aligned}
\begin{aligned} \sqrt{2}:1 \end{aligned}
\begin{aligned} \sqrt{3}:1 \end{aligned}

Answer: Option C

Explanation:

Let the radius of hemisphere and cone be R,
Height of hemisphere H = R.
So the height of the cone = height of the hemisphere = R
Slant height of the cone
\begin{aligned}
= \sqrt{R^2+R^2} \\
= \sqrt{2}R \\
\frac{\text{Hemisphere Curved surface area}}{\text{Cone Curved surface area}} = \\
\frac{2\pi R^2}{\pi *R*\sqrt{2}R} \\
= \sqrt{2}:1
\end{aligned}

1. The perimeter of one face of a cube is 20 cm. Its volume will be:

\begin{aligned} 125 cm^3 \end{aligned}
\begin{aligned} 400 cm^3 \end{aligned}
\begin{aligned} 250 cm^3 \end{aligned}
\begin{aligned} 625 cm^3 \end{aligned}

Answer: Option A

Explanation:

Edge of cude = 20/4 = 5 cm

Volume = a*a*a = 5*5*5 = 125 cm cube

2. If the volume of two cubes are in the ratio 27:1, the ratio of their edges is:

Answer: Option A

Explanation:

Let the edges be a and b of two cubes, then

\begin{aligned}
\frac{a^3}{b^3} = \frac{27}{1} \\
=> \left( \frac{a}{b} \right)^3 = \left( \frac{3}{1} \right)^3 \\
\frac{a}{b}=\frac{3}{1} \\
=> a:b = 3:1
\end{aligned}

3. A circular well with a diameter of 2 meters, is dug to a depth of 14 meters. What is the volume of the earth dug out.

\begin{aligned} 40 m^3 \end{aligned}
\begin{aligned} 42 m^3 \end{aligned}
\begin{aligned} 44 m^3 \end{aligned}
\begin{aligned} 46 m^3 \end{aligned}

Answer: Option C

Explanation:

\begin{aligned}
Volume = \pi r^2h \\
Volume = \left(\frac{22}{7}*1*1*14\right)m^3 \\
= 44 m^3
\end{aligned}

4. 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

5. How many bricks, each measuring 25cm11.25cm6cm, will be needed to build a wall 8m6m22.5m

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}