Introduction
Mensuration is one of important topic in Quantitative Aptitude Section. In Mensuration – Quiz 7 article candidates can find questions with answer. By solving this questions candidates can improve and maintain, speed, and accuracy in the exams. Mensuration – Quiz 7 questions are very useful for different exams such as IBPS PO, Clerk, SSC CGL, SBI PO, NIACL Assistant, NICL AO, IBPS SO, RRB, Railways, Civil Services etc.
Q1
In the figure, ABCD is a square with side 10. BFD is an arc of a circle with centre C. BGD is an arc of a circle with centre A. What is the area of the shaded region ?
- A. [latex]100 – 50 \pi[/latex]
B. [latex]100 – 25 \pi[/latex]
C. [latex]50 \pi - 100[/latex]
D. [latex]25 \pi - 100[/latex]
Area of the portion DFBC = [latex]\frac{1}{4} \times \pi \times {(10)}^{2} = 25 \pi[/latex]
i.e, Area of △BCD = [latex]\frac{1}{2} \times 10 \times 10 = 50 [/latex]
i.e, Area of the portion DFBOD = Area of the portion DFBC – Area of △BCD
= 25[latex]\pi[/latex] – 50
i.e, Area of the portion DFBGD
= 2 [latex]\times[/latex] Area of the portion DFBOD
= 2(25[latex]\pi[/latex] – 50) = 50[latex]\pi[/latex] – 100
Q2
An edge of a cube measures 10 cm. If the largest possible cone is cut out of this cube, then volume of the cone is
- A. 260 [latex]{cm}^{3}[/latex]
B. 260.9 [latex]{cm}^{3}[/latex]
C. 261.9 [latex]{cm}^{3}[/latex]
D. 262.7 [latex]{cm}^{3}[/latex]
Height of the cone = 10 cm
Radius of the base = [latex]\frac{10}{2}[/latex] cm = 5 cm
Hence volume of the largest possible cone cut out of this cube
= [latex]\frac{1}{3} \times \frac{22}{7} \times {(5)}^{2} \times 10 = 261.8 {cm}^{3}[/latex]
Q3
It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 440 cubic metres in 10 minutes. The inner radius of the pipe should be
- A. 3 m
B. 2 m
C. 4 m
D. 5 m
Volume of the pipe in one minute
= [latex] \pi \times {r}^{2}(7) = \frac{440}{10} [/latex]
r = 2
Q4
The weight of a solid cone having diameter 14 cm and vertical height 51 cm is ___, if the material of solid cone weighs 10 grams per cube cm.
- A. 16.18 kg
B. 17.25 kg
C. 26.18 kg
D. 71.40 kg
Volume of the solid cone = [latex]\frac{1}{3} \times \pi \times {7}^{2} \times 51[/latex]
= [latex]\frac{1}{3} \times \frac{22}{7} \times 49 \times 51[/latex] = 2618 [latex]{cm}^{3}[/latex]
i.e, Weight of the solid cone = (2618 [latex]\times [/latex] 10) gm.
= [latex]\frac{26180}{1000} kg[/latex] = 26.18 kg
Q5
A wire is looped in the form of a circle of radius 28 cm. It is re-bent into a square form. Determine length of the side of the square.
- A. 44 cm
B. 45 cm
C. 46 cm
D. 48 cm
Given : R = 28
Circumference = 2[latex]\pi[/latex](28) = 176
Side of the square = [latex]\frac{176}{4}[/latex] = 44