## 6.5.6 Volume of Three Dimensional Shapes, PT3 Practice

Question 14: Diagram shows a right cylinder with a diameter of ( y  + 4 ) cm. Given the volume of the cylinder is 269.5 cm3 and by using  find the value of it’s radius. [4 marks] Solution: volume of the cylinder = 269.5 πr2h = 269.5 22 7 × r 2 ×7=269.5 22 7 × … Read more

## 6.5.5 Volume of Three Dimensional Shapes, PT3 Practice

Question 13: Diagram shows a composite solid formed by joining a quarter cylinder and a cuboid which lies on the horizontal plane. It is given that the height of the cuboid is 9 cm and the volume of the composite solid is  1002 6 7  cm 3 .   Using  π= 22 7 , calculate … Read more

## 6.5.4 Volume of Three Dimensional Shapes, PT3 Practice

Question 11: Diagram shows a composite formed by joining a quarter cylinder and a right prism at the rectangular plane EFGH. The trapezium ABGF and the quarter circle FGK are the uniform cross sections of the solid. Using   π= 22 7 , calculate the volume, in  cm3, of the composite solid. Solution: Volume of FGK = 1 4 ( π … Read more

## 6.5.3 Volume of Three Dimensional Shapes, PT3 Practice

Question 8: A spherical balloon expands such that its volume increases from 36π cm3 to 288π cm3 . Find the increment of the radius, in cm, of the balloon. Solution: V 1 = 4 3 π r 1 3 4 3 π r 1 3 =36π r 1 3 =36π× 3 4π r 1 3 … Read more

## 6.5.2 Volume of Three Dimensional Shapes, PT3 Practice

Question 4: The cross section of the prism shown is an isosceles triangle.   The volume of the prism, in cm3, is Solution: Height of the △ = 10 2 − 6 2 = 64 = 8 c m Volume of prism = Area of cross section × Length = ( 1 2 × 12 … Read more

## 6.5.1 Volume of Three Dimensional Shapes, PT3 Practice

6.5.1 Volume of Three Dimensional Shapes, PT3 Practice Question 1: The diagram below shows a cone with diameter 14 cm and height 6 cm.   Find the volume of the cone, in cm3.   Solution: Volume of a cone = 1 3 π r 2 h = 1 3 × 22 7 × 7 2 … Read more

## 6.4.3 Surface Area of Three Dimensional Shapes, PT3 Focus Practice

Question 6: Diagram below shows a right pyramid with a square base. Calculate the total surface area, in cm2, of the right pyramid.   Solution: h2= 102 – 62    = 100 – 36    = 64 h = √64    = 8cm Total surface area of the right pyramid = (12 × 12) + 4 … Read more

## 6.4.2 Surface Area of Three Dimensional Shapes, PT3 Focus Practice

6.4.2 Surface Area of Three Dimensional Shapes, PT3 Focus Practice Question 4: Sphere below has a surface area of 221.76 cm2. Calculate its radius. ( π = 22 7 ) Solution: Surface area of sphere = 4πr2 4 π r 2 = 221.76 4 × 22 7 × r 2 = 221.76 r 2 = … Read more

## 6.4.1 Surface Area of Three Dimensional Shapes, PT3 Focus Practice

6.4.1 Surface Area of Three Dimensional Shapes, PT3 Focus Practice Question 1: Diagram below shows closed right cylinder. Calculate the total surface area, in cm2, of the cylinder.   ( π = 22 7 ) Solution: Total surface area = 2(πr2) + 2πrh = ( 2 × 22 7 × 7 2 ) + ( … Read more

## 6.3 Volume of Three Dimensional Shapes

6.3 Volume of Three Dimensional Shapes   6.3.1 Right Prisms and Right Circular Cylinders 1. 2. 6.3.2 Right Pyramids and Right Circular Cones 1. 2.   6.3.3 Spheres 1. 2.