MAH CET MCA Mensuration Previous Year Questions (PYQs)
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Showing 9 questions
A pendulum swings through an angle of $30^\circ$ and describes an arc of $17.6\ \text{cm}$ in length. Find the length of the pendulum.
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Solution
Arc length $l = r\theta$.
Here $\theta = 30^\circ = \dfrac{\pi}{6}\ \text{radians}$ and $l = 17.6$.
So, $r = \dfrac{l}{\theta} = \dfrac{17.6}{\pi/6} = \dfrac{17.6 \times 6}{3.14} \approx 33.6\ \text{cm}$.
Two cubes each of volume $64\ \text{cm}^3$ are joined end to end. Find the surface area of the resulting cuboid.
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Solution
Each cube side $a = \sqrt[3]{64} = 4\ \text{cm}$.
When joined end to end, dimensions of cuboid $= 8 \times 4 \times 4$.
Surface area $= 2(lb + bh + hl) = 2(8\times4 + 4\times4 + 4\times8) = 2(32 + 16 + 32) = 160\ \text{cm}^2$.
A circular wire of radius $7.5\ \text{cm}$ is cut and bent to lie along the circumference of a hoop of radius $120\ \text{cm}$. Find (in degrees) the angle subtended at the hoop’s centre.
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Solution
Arc length $s = 2\pi(7.5)=15\pi$.
On hoop of radius $120$, $\theta = \dfrac{s}{r} = \dfrac{15\pi}{120}=\dfrac{\pi}{8}=22^\circ 30'$.
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Two circles touch externally. The sum of their areas is 130$\pi$ sq.cm and
the distance between their centres is 14 cm. Find the radii of the circles.
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Solution
Calculate the area other than the area common between two quadrants of
circles of radius 16 cm each, which is shown as the shaded region in the
figure given.
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Solution
Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
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The curved surface area of a glass having radii 3cm and 4cm respectively and slant height 10cm is
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Solution
A cylinder of radius 12cm contains water to a depth of 20cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75cm. The radius of the ball is
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Solution
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