A circular piece of cardboard with a diameter of \(1\) m will be made into a conical hat \(40\) cm high by cutting a sector off and joining the edges to form a cone. Determine the angle subtended by the sector removed.
A\(144^\circ\)
B\(148^\circ\)
C\(152^\circ\)
D\(154^\circ\)
#2📜 CE Board November 1994
What is the area in sq. m of the zone of a spherical segment having a volume of \(1470.265\) cu. m if the diameter of the sphere is \(30\) m?
A\(465.5 \text{ m}^2\)
B\(565.5 \text{ m}^2\)
C\(665.5 \text{ m}^2\)
D\(656.5 \text{ m}^2\)
#3📜 CE Board May 1995
A sphere having a diameter of \(30\) cm is cut into \(2\) segments. The altitude of the first segment is \(6\) cm. What is the ratio of the area of the second segment to that of the first?
A4:1
B3:1
C2:1
D3:2
#4📜 CE Board November 1996
If the edge of a cube is increased by \(30\%\), by how much is the surface area increased?
A30%
B33%
C60%
D69%
#5📜 ECE Board April 1995
Each side of a cube is increased by \(1\%\). By what percent is the volume of the cube increased?
A1.21%
B2.8%
C3.03%
D3.5%
#6📜 ECE Board November 1992
Given a sphere of diameter, d. What is the percentage increase in its diameter when the surface area increases by \(21\%\)?
A5%
B10%
C21%
D33%
#7📜 ECE Board November 1992
Given a sphere of diameter, d. What is the percentage increase in its volume when the surface area increases by \(21\%\)?
A5%
B10%
C21%
D33%
#8📜 EE Board October 1991
How many times does the volume of a sphere increases if the radius is doubled?
A4 times
B2 times
C6 times
D8 times
#9📜 CE Board May 1997
A circular cone having an altitude of \(9\) m is divided into \(2\) segments having the same vertex. If the smaller altitude is \(6\) m, find the ratio of the volume of the small cone to the big cone.
A0.186
B0.296
C0.386
D0.486
#10📜 CE Board November 1997
Find the volume of a cone to be constructed from a sector having a diameter of \(72\) cm and a central angle of \(210^\circ\).
A\(12367.2 \text{ cm}^3\)
B\(13232.6 \text{ cm}^3\)
C\(13503.4 \text{ cm}^3\)
D\(14682.5 \text{ cm}^3\)
#11📜 CE Board May 1998
Find the volume of a cone to be constructed from a sector having a diameter of \(72\) cm and a central angle of \(150^\circ\)
A\(5533.32 \text{ cm}^3\)
B\(6622.44 \text{ cm}^3\)
C\(7710.82 \text{ cm}^3\)
D\(8866.44 \text{ cm}^3\)
#12📜 CE Board November 1996
A conical vessel has a height of \(24\) cm and a base diameter of \(12\) cm. It holds water to a depth of \(18\) cm above its vertex. Find the volume (in \(\text{cm}^3\)) of its content.
A188.40
B298.40
C381.70
D412.60
#13📜 CE Board May 1995
What is the height of a right circular cone having a slant height of \(\sqrt{10x}\) and a base diameter of \(2x\)?
A\(2x\)
B\(3x\)
C\(3.317x\)
D\(3.162x\)
#14📜 CE Board November 1995
The ratio of the volume to the lateral area of a right circular cone is 2:1. If the altitude is \(15\) cm, what is the ratio of the slant height to the radius?
A5:6
B5:4
C5:3
D5:2
#15📜 CE Board November 1994
A regular triangular pyramid has an altitude of \(9\) m and a volume of \(187.06\) cu. m. What is the base edge in meters?
A12
B13
C14
D15
#16📜 CE Board November 1995
The volume of the frustum of a regular triangular pyramid is \(135\) cu. m. The lower base is an equilateral triangle with an edge of \(9\) m. The upper base is \(8\) m above the lower base. What is the upper base edge in meters?
A2
B3
C4
D5
#17📜 EE Board April 1992
What is the volume of a frustum of a cone whose upper base is \(15\) cm in diameter and lower base \(10\) cm. in diameter with an altitude of \(25\) cm?
A\(3018.87 \text{ cm}^3\)
B\(3180.87 \text{ cm}^3\)
C\(3108.87 \text{ cm}^3\)
D\(3081.87 \text{ cm}^3\)
#18📜 EE Board April 1993
In a portion of an electrical railway cutting, the areas of cross section taken every \(50\) m are \(2556\), \(2619\), \(2700\), \(2610\) and \(2484\) sq. m. Find its volume.
A\(522{,}600 \text{ m}^3\)
B\(520{,}500 \text{ m}^3\)
C\(540{,}600 \text{ m}^3\)
D\(534{,}200 \text{ m}^3\)
#19📜 ME Board April 1996
Determine the volume of a right truncated triangular prism with the following definitions: Let the corners of the triangular base be defined by A, B and C. The length of \(AB = 10\) ft., \(BC = 9\) ft. and \(CA = 12\) ft. The sides A, B and C are perpendicular to the triangular base and have the height of \(8.6\) ft., \(7.1\) ft. and \(5.5\) ft. respectively.
A\(413 \text{ ft}^3\)
B\(311 \text{ ft}^3\)
C\(313 \text{ ft}^3\)
D\(391 \text{ ft}^3\)
#20📜 CE Board November 1995
A circular cylinder with a volume of \(6.54\) cu. m is circumscribed about a right prism whose base is an equilateral triangle of side \(1.25\) m. What is the altitude of the cylinder in meters?
