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📘 1001 Math RojasMedium
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 November 1996📘 1001 Math RojasMedium
If the edge of a cube is increased by \(30\%\), by how much is the surface area increased?
A30%
B33%
C60%
D69%
#4📜 ECE Board April 1995📘 1001 Math RojasMedium
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%
#5📜 ECE Board November 1992📘 1001 Math RojasMedium
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%
#6📜 CE Board November 1997📘 1001 Math RojasMedium
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\(14682.5 \text{ cm}^3\)
#7📜 CE Board May 1998📘 1001 Math RojasMedium
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\(8866.44 \text{ cm}^3\)
#8📜 CE Board November 1996📘 1001 Math RojasMedium
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
#9📜 CE Board May 1995📘 1001 Math RojasMedium
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\(3.162x\)
#10📜 CE Board November 1995📘 1001 Math RojasMedium
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
#11📜 CE Board November 1994📘 1001 Math RojasMedium
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
#12📜 EE Board April 1992📘 1001 Math RojasMedium
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\(3081.87 \text{ cm}^3\)
#13📜 ME Board April 1996📘 1001 Math RojasMedium
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\(391 \text{ ft}^3\)
#14📜 CE Board November 1995📘 1001 Math RojasMedium
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?
A3.50
B3.75
C4.00
D4.25
#15📜 CE Board May 1996📘 1001 Math RojasMedium
A circular cylinder is circumscribed about a right prism having a square base one meter on an edge. The volume of the cylinder is \(6.283\) cu.m. Find its altitude in meters.
A4.00
B3.75
C3.50
D3.25
#16📜 CE Board November 1997📘 1001 Math RojasMedium
The bases of a right prism is a hexagon with one of each side equal to \(6\) cm. The bases are \(12\) cm apart. What is the volume of the right prism?
A\(1211.6 \text{ cm}^3\)
B\(2211.7 \text{ cm}^3\)
C\(1212.5 \text{ cm}^3\)
D\(1122.4 \text{ cm}^3\)
#17📘 1001 Math RojasMedium
A regular octahedron has an edge \(2\) m. Find its volume (in \(\text{m}^3\))
A3.77
B1.88
C3.22
D2.44
#18📜 CE Board November 1996📘 1001 Math RojasMedium
The volume of water in a spherical tank having a diameter of \(4\) m is \(5.236 \text{ m}^3\). Determine the depth of the water in the tank.
A1.0
B1.2
C1.4
D1.8
#19📜 CE Board May 1997📘 1001 Math RojasMedium
The corners of a cubical block touched the closed spherical shell that encloses it. The volume of the box is \(2744\) cubic cm. What volume in cubic centimeter inside the shell is not occupied by the block?
A2714.56
B3714.65
C4713.56
D4613.74
#20📜 Preboard📘 PowerhouseMedium
The volume of a cube becomes three times when its edge is increased by 1 inch. What is the edge of the cube?
