The figure below is a cone whose base radius is 3.5cm and slant height 7cm. The net of the cone is a sector of a circle.(a) Find the angle subtended at the centre of the sector. (2mks)(b) Draw the net of the solid. (1mk)
A bucket is in the shape of a frustrum with base radius 12cm and top radius 16cm. the slant height of the bucket is 30cm as shown below. The bucket is full of water.a) Calculate the volume of the water. (Take = 3.142) (6mks)b) All the water is poured into a cylindrical container of circular radius 12cm. If the cylinder has height 45cm, calculate the surface area of the cylinder which is not in contact with water (4mks)
Worked Solution:The figure above is a triangular prism of uniform cross – section in which AF = 4cm, AB = 5cm and BC = 8cm.a) If a triangle BAF = 30^{0}, calculate the surface area of the prism (3mks)b) Draw a clearly labelled net of the prisms (1mk)Worked Answer:Two similar cans have different heights 8cm and other one 10cm. If the surface area of the larger can is 480cm^{3}, find the surface area of the smaller can (3mks)Worked Answer:
Form 2 Mathematics
A school water tank is in the shape of a frustum of a cone. The height of the tank is 7.2 m and the top and bottom radii are 6m and 12 m respectively.
(a) Calculate the area of the curved surface of the tank, correct to 2 decimal places. (b) Find the capacity of the tank, in litres, correct to the nearest litre. (c) On a certain day, the tank was filled with water. If the school has 500 students and each student uses an average of 40 litres of water per day, determine the number of days that the students would use the water. Form 2 MathematicsA cylindrical piece of wood of radius 4.2 cm and length 150 cm is cut length into two equal pieces. Calculate the surface area of one piece (Take ∏ as ^{22}/_{7} (4mks) Form 2 Mathematics
A solid S is made up of a cylindrical part and a conical part. The height of the solid is 4.5 m.
The common radius of the cylindrical part and the conical part is 0.9 m. The height of the conical part is 1.5 m. (a). Calculate the volume. correct to 1 decimal place, of solid S. (b). Calculate the total surface area of solid S. A square base pillar of side 1.6 m has the same volume as solid S. Determine the height of the pillar, correct to 1 decimal place. Form 2 Mathematics
The figure below represents a model of a solid structure in the shape of a frustum of a cone with hemispherical top. The diameter of the hemispherical part is 70cm and is equal to the diameter of the top of the frustum. The frustum has a base diameter of 28cm and slant height of 60cm.
Calculate
Form 2 Mathematics
The figure below represents a conical flask. The flask consists of a cylindrical part and a frustum of a cone. The diameter of the base is 10cm while that of the neck is 2 cm. the vertical height of the flask is 12cm.
Calculate, correct to 1 decimal place
a) The slant height of the frustum part b) The slant height of the smaller cone that was cut off to make the frustum part c) The external surface area of the flask. (Take π =3.142) Form 2 Mathematics
The figure below shows a right pyramid VABCDE. The base ABCDE is regular pentagon. AO = 15cm and VO = 36 cm.
Calculate:
(a) The area of the base correct to 2 decimal places (b) The length AV (c) The surface area of the correct to 2decimal places (d) The volume of the pyramid correct to 4 significant figures Form 2 Mathematics
The figure below represents a cone of height 12 cm and base radius of 9 cm from which a similar smaller cone is removed, leaving a conical hole of height 4 cm.
a) Calculate:
i. The base radius of the conical hole; ii. The volume, in terms of π, of the smaller cone that was removed. b) (i) Determine the slant height of the original cone. (ii) Calculate, in terms of it, the surface area of the remaining solid after the smaller cone is removed. Form 2 MathematicsForm 2 Mathematics
The length of a solid prism is 10cm. Its cross section is an equilateral triangle of side 6cm.
Find the total surface area of the prism. Form 2 Mathematics
The figure below represents a solid cuboid ABCDEFGH with a rectangular base, AC= 13cm, BC = 5 cm and CH = 15cm.
(a) Determine the length of AB,
(b) Calculate the surface area of the cuboid. (c) Given that the density of the material used to make the cuboid is 7.6 g/cm3, calculate its mass in kilograms. (d) Determine the number of such cuboids that can fit exactly in a container measuring 1.5 m by 1.2 m by 1 m. Form 2 Mathematics
A solid consists of a cone and a hemisphere. The common diameter of the cone and the hemisphere is 12 cm and the slanting height of the cone is 10 cm.
(a) Calculate correct to two decimal places: (i) the surface area of the solid; (ii) the volume of the solid (b) If the density of the material used to make the solid is 1.3 g/cm^{3}, calculate its mass in kilograms. Form 2 Mathematics
A rectangular box open at the top has a square base. The internal side of the base is x cm long and the total internal surface area of the box is 432 cm^{2}.
(a) Express in terms of x: (i) the internal height h, of the box; (ii) the internal volume V, of the box. (b) Find: (i) the value of x for which the volume V is maximum; (ii) the maximum internal volume of the box. Form 2 Mathematics
A cylindrical solid whose radius and height are equal has a surface area of 154 cm^{2}. Calculate its diameter, correct to 2 decimal places. (Take π = 3.142)
Form 2 Mathematics
A glass, in the form of a frustum of a cone, is represented by the diagram below.
The glass contains water to a height of 9 cm,. The bottom of the glass is a circle of radius 2 cm while the surface of the water is a circle of radius 6 cm.
a) Calculate the volume of the water in the glass
b) When a spherical marble is submerged into the water in the glass, the water level rises by 1 cm. Calculate: i) The volume of the marble; ii) The radius of the marble Form 2 Mathematics
A rectangular and two circular cutouts of metal sheet of negligible thickness are used to make a closed cylinder. The rectangular cutout has a height of 18cm. Each circular cuout has a radius of 5.2cm. Calculate in terms of pi, the surface area of the cylinder
Form 2 MathematicsForm 2 Mathematics
The figure below is a model representing a storage container. The model whose total height is 15cm is made up of a conical top, a hemispherical bottom and the middle part is cylindrical. The radius of the base of the cone and that of the hemisphere are each 3cm. The height of the cylindrical part is 8cm.
(a) Calculate the external surface area of the model
(b) The actual storage container has a total height of 6 metres. The outside of the actual storage container is to be painted. Calculate the amount of paint required if an area of 20m^{2} requires 0.75 litres of the paint Form 2 MathematicsForm 2 Mathematics  Topical Questions and Answers
A solid made up of a conical frustum and a hemisphere top as shown in the figure below. The dimensions are as indicated in the figure.
Related Questions on Surface area of SolidsFree 1999 K.C.S.E Mathematics Topical Question & Answers Paper 1
An open right circular cone has a base radius of 5 cm and a perpendicular height of 12 cm.
Calculate the surface area of the cone ( take Î to be 3.142)

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