Test paper -7
1) The total surface area of a cube is 150cm½. Its volume is
a) 216 cm³ b) 125 cm³ c) 64 cm³ d) 1000 cm³
2) The volume of a cube is 343 cm³. Its total surface area is
a) 196cm² b) 49 cm² c) 294 cm² d) 147cm²
3) The cost of painting the whole surface area of a cube at the rate of 10 paise per cm² is Rs 264.60. Then the volume of the cube is
a) 6859 cm³ b) 9261 cm³ c) 8000 cm³ d) 10648 cm³
4) How many bricks, each measuring 25cm x 11.25cm x 6 cm, will be needed to build a wall 8m long, 6m high and 22.5 m thick?
a) 5600 b) 6000 c) 6400 d) 7200
5) How many cubes are 10cm edge can be put in a cubical box upon 1m edge ?
a) 10 b) 100 c) 1000 d) 10000
6) The edge of a cuboid are in the ratio 1:2:3 and its surface area is 88 cm². The volume of the cuboid is
a) 48 cm³ b) 64cm³ c) 96 cm³ d) 120 cm³
7) Two cubes have their volumes in the ratio 1:27. The ratio of the surface area is
a) 1:31 b) 1:9 c) 1:27 d) none
8) The surface area of a (10cm x 4cm x 3cm) brick is
a) 84cm² b) 124 cm² c) 164cm² d) 180cm²
9) An iron beam is 9m long, 40cm wide and 20cm height. if one cubic meter of iron weigh 50 kg. What is the weight of the beam?
a( 56kg b) 48kg c) 36kg d) 27kg
10) A rectangular water reservoir contains 42000 litres of water. If the length of reservoir is 6m and its breadth is 3.5m, the depth of The reservoir is
a) 2m b) 5m c) 6m d) 8m
11) The dimension of a room are (10m x 8m x 3.3m). How many men can be accommodated in this room. If each men required 3 m³ of space ?
a) 99 b) 88 c) 77 d) 75
12) A rectangular water tank is 3m long, 2m wide and 5m high. How many litres of water can it hold ?
a) 30000 b) 15000 c) 25000 d) 35000
13) The area of the cardboard needed to make a box of size 25cm x 15cm x 8cm will be
a) 390cm² b) 1390cm² c) 2780cm² d) 1000 cm²
14) The diagonal of a cube measures 4√3 cm. Its volume is
a) 8 cm³ b) 16 cm³ c) 27 cm³ d) 64 cm³
15) The diagonal of a cube is 9√3cm long . Its total surface area is
a) 243cm² b) 486cm² c) 324cm² d) 648cm²
16) If each side of a cube is doubled then its volume
a) is doubled b) becomes 4 times c) becomes 6 times d) becomes 6 times
17) If each side of a cube is doubled. its surface area
a) is doubled b) becomes 4 times c) becomes 6 times d) becomes 8 times
respectively in the following 16-18 5 equal to switch off 85 + addition to each other the volume of the cuboids of form is 125 375 25625 a circular way with diameter 2 with double what is the volume of the each dog out
Test paper -6
1) If a and b are rational numbers and (2+√3)/(2-√3)= a + b √3, find the values of a and b.
2) Simplify: (3√2/(√6+√3) + √6/(√3+√2) - 4√3/(√6+√2).
3) Rationalize: √2/(√2+√3-√5).
4) A room is half as a long again as it is broad. The cost of carpeting the room 18 at Rs 18 per m² is Rs 972 and the cost of white washing the four walls at Rs 6 per m² is Rs 1080. Find the dimension of the room.
5) A field is 80m long and 50m broad. In one corner of the field, a pit which is 10m long, 7.5m broad and 8m deep has been dug out. The earth taken out of it is evenly spread over the remaining part of the field. Find the rise in the level of the field.
6) Find the volume, and the total surface area, the lateral surface area and the length of the diagonal of a cube each of whose edge measure 20cm.
7) The total surface area of a cube is 726cm². Find its volume.
8) Two poles of height 9m and 14m stand vertically on a plane ground. If the distance between their feet is 12m, find the distance between their tops.
9) In a rhombus ABCD, prove that: AB²+ BC²+ CD²+ AD²= AC²+ BD².
10) A ladder 17 m long reaches the window of a building 15m above the ground. Find the distance of the foot of the ladder from the building.
11) The sides of a triangle containing the right angle are 5xcm and (3x -1) cm. if the area of the triangle is 60cm², calculate the length of the sides of the triangle.
12) Find the altitude of an equilateral triangle of side 5√3cm.
1) ABCD represents a plot of land owned by man.
He divides it into two parts by joining diagonal BD and donate the triangular part BAD to an orphanage .
i) If angle CBD=90°, find the area of the plot donated by him.
ii) What are the values shown by the man here ?
2) Some students started a cleanliness campaign in their school. For distribution among the fellow students, they prepared hand fans by stitching 10 equal sized triangular strips of different types of paper (as shown in the given figure).
The dimensions of equal strips are 25cm, 14cm and 25 cm. They wrote slogans for maintaining cleanliness in shaded areas.
i) Find the area used for writing the slogans.
ii) What value are depicted by the students?
3) The diagram given below shows the triangular side walls of the entrance to a library with quotes by Mahatma Gandhi written on them. The sides of each of the triangular walls are 15m, 11m and 6m respectively.
a) Find the area of each of the triangular wall.
b) What values can be inculcated by the two quotes in the visitors ?
4) A woman inherits a triangular plot of land ABC as shown in the figure.
She contributes to society by donating a triangular piece ADC out of this plot for constructing an old age.
i) Find the area of the plot with her.
ii) What values are shown by the woman?
UNIT TEST - A
MM- 10
(1 Mark each)
1) A triangle ABC in which AB= AC = 4cm and angle A= 90°, has an area of
a) 4cm² b) 16cm² c) 8cm² d) 12cm²
2) The area of a triangle whose sides are 8cm,15 cm and 19 cm is
a) 91√19cm² b) 6√91 cm² c) 19√91cm² d) 8√91cm²
3) Find the area of an equilateral triangle whose perimeter 18 cm. (Take √3= 1.732). (2)
4) Find the area that needs to be added to the area ∆ ADB,
so that it become equal to the area of ∆ ABC (take √3= 1.732). (3)
5) Find the area of ∆ ABC in which AB= 36cm, BC = 48cm and AC= 60cm. Find the length of the shortest altitude. (3)
BOOSTER - A
1) The area of the triangle with the base 8cm and height 10cm is
a) 80cm² b) 40cm² c) 20cm² d) 18 cm²
2) The sides of a triangle are 12cm, 16cm and 20 cm. Its area is
a)48cm² b) 120cm² c) 96 cm² d) 160 cm²
3) The area of a triangle whose sides are 3cm, 4cm and 5cm is
a) 42cm² b) 6cm² c) 84cm² d) 100cm²
4) If the perimeter of an equilateral triangle is 24m, then its area is
a) 20√3m² b) 16√3m² d) 8√3 m² d) 24√3 m²
5) If the area of the equilateral triangle is 16√3cm², then the perimeter of the triangle is
a) 12cm b) 24cm c) 48cm d) 36cm
6) the edges of a triangle board are 6cm, 8cm and 10 cm. The cost of painting it at the rate of 70 paise per cm² is
a) Rs 7 b) Rs 16.80 c) Rs 17 d) Rs 16
7) The perimeter of a Rhombus is 20cm. If one of its diagonals is 6cm, then its area is
a) 28 cm² b) 36cm² c) 24 cm² d) 20cm²
8) An isosceles right triangle has an area 8cm². The length of the hypotenuse is
a) 6cm b) √32cm c) 8cm d) 4cm
9) The area of an isosceles triangle having base 24 cm and length of one of the equal side is 20cm is
a) 480cm² b) 196cm² c) 240cm² d) 192cm²
10) The perimeter of an isosceles triangle is 32 cm. The ratio of equal side to its base is 3:2. Then area of the triangle is
a) 32√2 cm² b) 32cm² c) 16 √2cm² d) 16cm²
11) If the perimeter and base of an isosceles triangle are 11cm and 5cm respectively, then it's area is
a) 5√11cm² b) 5√11/2 cm² c) 5√11/8 cm² d) 5√11/4 cm²
12) If the difference between the semi-perimetre 's' and the sides 'a', 'b' and 'c' of ∆ ABC are 8cm, 7 cm and 6cm respectively, then ar(∆ ABC) is
a) 63cm² b) 42 cm² c) 84 cm² d) 168 cm²
13) thre sides of a triangle are 13cm, 14cm and 15cm. The length of the shortest altitude is
a) 12cm b) 11.2cm c) 12.9cm d) 11.9cm
14) The sides of a triangle are 17cm, 25cm and 26cm. The length of the altitude to the longest side correct up to two places of decimals is
a) 16.32cm b) 34.00cm c) 15.69cm d) 24.00cm
15) If the perimeter of rhombus whose diagonals measure by 12cm and 16 cm is equal to the perimeter of an isosceles triangle having the equal side and the base in the ratio 3:2, then the area of the isosceles triangle is
a) 500√2cm² b) 25√2 cm² c) 75√2 cm² d) 100√2cm²
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