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Question Detail
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
1. 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
2. The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km square. The height of mountain is :
- 2.3 km
- 2.4 km
- 2.5 km
- 2.6 km
Answer: Option B
Explanation:
Let the radius of the base be r km. Then,
\begin{aligned}
\pi r^2 = 1.54 \\
r^2 = \frac{1.54*7}{22} = 0.49\\
= 0.7 km \\
\text{Now l=2.5 km, r = 0.7 km} \\
h = \sqrt{2.5^2 - 0.7^2} km \\
=\sqrt{6.25 - 0.49}\\
=\sqrt{5.76} km \\
= 2.4 km
\end{aligned}
3. A cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm. The percentage of the wood wasted is :
- 45%
- 56%
- 67%
- 75%
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}
4. 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}
5. There are bricks with 24 cm x 12 cm x 8 cm dimensions. Find the total number of bricks required to construct a wall 24 m long, 8 m high and 60 m thick with 10% of wall filled with mortar.
- 35000
- 40000
- 45000
- 50000
Answer: Option C
Explanation:
So as per question,
\begin{aligned}
\text{Volume of wall} = (2400 * 800 * 60 ) cm^3 \\
\text{Volume of bricks} = \text { 90% of volume of wall } \\
= [ \frac{90}{100} * 2400 * 800 * 60 ] cm^3 \\
\text{ Volume of 1 brick = } (24 * 12 * 8) cm^3 \\
\text{Number of Bricks required} \\
= \frac{ (\frac{90}{100}) * (2400 * 800 * 60)}{24 * 12 * 8} \\
= 45000
\end{aligned}
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