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.

Answer: Option A

Explanation:

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

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

Answer: Option C

Explanation:

We will first calculate the Surface area of cube, then we will calculate the quantity of paint required to get answer.
Here we go,

$$\begin{aligned} \text{Surface area =}6a^2 \\ = 6 * 8^2 = 384 \text{sq feet} \\ \text{Quantity required =}\frac{384}{16} \\ = 24 kg\\ \text{Cost of painting =} 36.50*24 \\ = Rs. 876 \end{aligned}$$

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

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.

$$\begin{aligned} \text{Sphere Volume =}\frac{4}{3}\pi r^3 \\ \text{Cone Volume =}\frac{1}{3}\pi r^2h\\ \text{Volume of wood wasted =}\\ \left(\frac{4}{3}\pi *9*9*9\right)-\left(\frac{1}{3}\pi *9*9*9\right) \\ = \pi *9*9*9 cm^3 \\ \text{Required Percentage =} \\ \frac{\pi *9*9*9}{\frac{4}{3}\pi *9*9*9}*100 \% \\ = \frac{3}{4}*100 \% \\ = 75\% \end{aligned}$$

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.
$$\begin{aligned} \frac{1}{3}*\pi *r^2*h = 1232 \\ \frac{1}{3}*\frac{22}{7}*r^2*24 = 1232 \\ r^2 = \frac{1232*7*3}{22*24} = 49 \\ r = 7 \\ \text{Now, r = 7cm and h = 24 cm } \\ l = \sqrt{r^2+h^2} \\ = \sqrt{7^2+24^2} = 25cm \\ \text{Curved surface area =}\pi rl\\ = \frac{22}{7}*7*25 = 550 cm^2 \end{aligned}$$