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Question Detail
The curved surface of a right circular cone of height 15 cm and base diameter 16 cm is:
- \begin{aligned} 116 \pi cm^2 \end{aligned}
- \begin{aligned} 122 \pi cm^2 \end{aligned}
- \begin{aligned} 124 \pi cm^2 \end{aligned}
- \begin{aligned} 136 \pi cm^2 \end{aligned}
Answer: Option D
Explanation:
\begin{aligned}
\text{Curved surface area of cone=}\pi rl\\
l = \sqrt{r^2+h^2} \\
l = \sqrt{8^2+15^2} = 17cm \\
\text{Curved surface area =}\pi rl\\
= \pi *8*17 = 136 \pi cm^2
\end{aligned}
1. How many bricks, each measuring 25cm*11.25cm*6cm, will be needed to build a wall 8m*6m*22.5m
- 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}
2. 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
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. If the volume of two cubes are in the ratio 27:1, the ratio of their edges is:
- 3:1
- 3:2
- 3:5
- 3:7
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}
5. 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
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