Question Detail

12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. Find the diameter of each sphere.

4 cm
6 cm
8 cm
10 cm

Answer: Option A

Explanation:

In this type of question, just equate the two volumes to get the answer as,
\begin{aligned}
\text{Volume of cylinder =}\pi r^2h\\
\text{Volume of sphere =} \frac{4}{3}\pi r^3\\
=> 12*\frac{4}{3}\pi r^3 = \pi r^2h \\
=> 12*\frac{4}{3}\pi r^3 = \pi *8*8*2 \\
=> r^3 = \frac{8*8*2*3}{12*4} \\
=> r^3 = 8 \\
=> r = 2 cm \\
=> \text{Diameter =}2*2 = 4 cm
\end{aligned}

1. Find the surface area of a 10cm4cm3cm 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

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. 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}

4. A cylindrical tank of diameter 35 cm is full of water. If 11 litres of water is drawn off, the water level in the tank will drop by:

\begin{aligned} 11\frac{3}{7} cm \end{aligned}
\begin{aligned} 11\frac{2}{7} cm \end{aligned}
\begin{aligned} 11\frac{1}{7} cm\end{aligned}
\begin{aligned} 11 cm\end{aligned}

Answer: Option A

Explanation:

Let the drop in the water level be h cm, then,

\begin{aligned}
\text{Volume of cylinder= }\pi r^2h \\
=> \frac{22}{7}*\frac{35}{2}*\frac{35}{2}*h = 11000 \\
=> h = \frac{11000*7*4}{22*35*35}cm\\
= \frac{80}{7}cm\\
= 11\frac{3}{7} cm
\end{aligned}