MATHEMATICS EXAMINATION PAPER
Q1. Choose the correct option. (10 × 1 = 10 marks)
Q2. Write down short answers of following questions. (15 × 2 = 30 marks)
1Three similar drinking glasses have heights 7.5cm, 9cm and 10.5cm. If the tallest glass holds 343 milliliters, find the capacities of the other two.
2Define the shape Polygon. Also give example.
3In the triangles XBC and XDE, find the value of x and y. (Example 2)
4Find whether the parallelograms are similar given that one of the angle between sides is 45° in both the parallelograms. (Example 4)
5In triangle ABC, the sides are given as \( mBC = 9cm \), \( mAB = 6cm \) and \( mCA = 12cm \). In triangle DEF, the sides are given as \( mFD = 21cm \), \( mEF = 15.75cm \) and \( mDE = 10.5cm \). Prove that the triangles are similar.
6In the given figure, \( \triangle ABC \sim \triangle DEF \), \( mAB = 12cm \), \( mAC = 20cm \), \( mBC = 16cm \). In \( \triangle DEF \), \( mDE = 6cm \). Find \( mDF \) and \( mEF \).
7Find the value of x of the following:
8Two polygons are similar with a ratio of corresponding sides being 2:3. If the area of the smaller polygon is 54cm², find the area of the larger polygon. (Example 7)
9Find the unknowns in the following figures:
10Find the unknowns in the following figures:
11Find the unknowns in the following figures:
12Quadrilaterals ABCD and EFGH are similar, with a scale factor 3:4. If the area of quadrilateral ABCD is 64cm², find the area of quadrilateral EFGH.
13Two right cones have volumes in ratio 64:125. What is the ratio of: (a) Their heights (b) Their base areas
14With 5:3 ratio in height of similar water tankers, find volume of larger tanker in cubic meter if smaller tanker has volume of 270 cubic meters.
15Find the missing value of the following similar solids:
Q3. Write detailed answers of the following questions. (Answer any 2) (2 × 5 = 10 marks)
1. Find the unknown value in the following: (Example 6)
The quadrilaterals PQRS and XYZW are similar where \( mPQ = 35 \) and \( mXY = 25 \)
2. The ratio of the corresponding lengths of two similar cylindrical cans is 3:2. (Example 12)
(i) The larger cylindrical can has surface area of 67.5 m². Find the surface area of the smaller cylindrical can.
(ii) The smaller cylindrical can has a volume of 132 m³. Find the volume of larger tin can.
3. The ratio of the corresponding lengths of two similar conical cans is 3:2
(i) The larger conical can has surface area of 96 m². Find the surface area of the smaller conical can.
(ii) The smaller conical can has a volume of 240 m³. Find the volume of larger conical can.