1449/1 – 1 hour 15 minutes40 objective questions

1449/2 – subjective11 compulsory questions4 out of 5 questions 2 Hours 30 minutes

SCIENTIFIC CALCULATORGEOMETRICAL SET

4 marks

Solid Geometry & Volume

Combination of two solid geometry

1. Determine the two solids involved

2.Choose the operations + or -

3.Write the correct formulae

4.Substitute the values of r, h, d

Use 7

22

Try this A hemisphere PQR has taken out from the cyclinder. Find the volume of the remaining solid.

32

3

2rhr

P

Q

R

10 cm

8 cm

Cylinder - hemisphere

5557

22

3

2855

7

22

3

2366

The diagram shows a solid cone with radius 9 cmand height 14 cm. A cylinder with radius 3 cm and height 7 cm is taken out of the solid.

Calculate the volume,in cm3 , of theremaining solid.

Use 7

22

Diagram 3 shows a solid cone with radius 9 cm andheight 14 cm. A cylinder with radius 3 cm and height 7cm is taken out of the solid.

14 cm

9 cm

7 cm

3 cm

2

3

1rVcone

hrVcylinder2

Write the formula first

2

2

1

31 22

9 143 7

1188

coneV r h

2

2223 7

7

198

cylinderV r h

Remaining solid

= 1188 – 198

= 990

CIRCLES : Perimeter and Area

7

22

1. Use the correct formulae

2. Substitute with the correct values.

V

S

P

R6 cm

T

6 cm

9 cm

30O

7 cm

6 cm

U

Q

W

a) Find the perimeter of the shaded region

b) Calculate the area of the shaded region

V

S

P

R6 cm

T

6 cm

9 cm

30O

7 cm

6 cm

U

Q

W

Perimeter = PU + UV + VQ + ( PQ – ST ) + SWT

Area = area of triangle – area of hemisphere – area of the sector

(a).

Perimeter = PU + UV + VQ + ( PQ – ST ) + SWT

2

7

7

222

360

1807966

7

222

360

309

7

218

7

131 14.31

2

7

7

222

360

1807966

7

222

360

309

7

218

(b).

2

2

67

22

360

30

2

7

7

22

360

180912

2

1

28

709

28

925 32.25

Area

b)

a)

2

2

67

22

360

30

2

7

7

22

360

180912

2

1

28

709

2

7

7

222

360

1807966

7

222

360

309

7

218

Answers are in the wrong position

Diagram 4 shows two sectors ORST and OUV with the same centre O. RWO is a semicircle with diameter RO and RO=2OV. ROV and OUT are straight lines. OV=7cm and angle UOV= 60˚

Calculate

(a) perimeter of the whole diagram ,(b) area of the shaded region.

U

T

S

W

OR V7cm14cm

60o

7cm

3

264

77

222

360

60

7147

222

360

120714

)

UVTURSTOVROperimetera

Stress on the correct substitution of the values

154

77

22

360

180

147

22

360

1207

7

22

360

60

)

2

22

OWRORSTOUVareab

Stress on the correct substitution of the values

Diagram 4 shows two sectors ORST and OUV with the same centre O. RWO is a semicircle with diameter RO and RO=2OV. ROV and OUT are straight lines. OV=7cm and angle UOV= 60˚

Calculate

(a) perimeter of the whole diagram ,(b) area of the shaded region.

U

T

S

W

OR V7cm14cm

60o

7cm

3

264

77

222

360

60

7147

222

360

120714

)

UVTURSTOVROperimetera

Stress on the correct substitution of the values

154

77

22

360

180

147

22

360

1207

7

22

360

60

)

2

22

OWRORSTOUVareab

Stress on the correct substitution of the values