VOLUME AND SURFACE AREA OF COMBINED SHAPES QUESTIONS

Question 1 :

A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter is 14 cm and the height of the vessel is 13 cm. Find the capacity of the vessel.

Solution :

Height of vessel  =  13 cm

radius of hemisphere + height of cylinder  =  13

7 + h  =  13

h  =  13 - 7  =  6 cm

Volume of vessel 

  =  volume of hemisphere + volume of cylinder

  =  (2/3)πr³ + πr² h

  =  πr²[(2/3) r + h]

  =  (22/7) 7²[(2/3) 7 + 6]

  =  (22/7) 49 (32/3)

  =  1642.67 cm³

Question 2 :

Nathan, an engineering student was asked to make a model shaped like a cylinder with two cones attached at its two ends. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of the model that Nathan made.

Solution :

Volume of model  =  2 volume of cones + volume of cylinder

  =  2 (1/3)πr²h + πr²h

Height of the model  =  12 

2(height of cone) + height of cylinder  =  12

2(2) + h  =  12

height of cylinder  =  8 cm

  =  πr²[(2/3) 2 + 8]

  =  (22/7) (3/2)²[(4/3) + 8]

=  (22/7) (9/4) (28/3)

Volume of model  =  66 cm³

Question 3 :

From a solid cylinder whose height is 2.4 cm and the diameter 1.4 cm, a cone of the same height and same diameter is carved out. Find the volume of the remaining solid to the nearest cm³ .

Solution :

Volume of remaining solid  =  Volume of cylinder - Volume of cone

  =  πr²h - (1/3) πr²h

  =  πr²h[1 - (1/3)]

  =  (22/7)(0.7)²(2.4) (2/3)

  =  (22/7)(0.7)²(2.4) (2/3)

  =  2.46 cm³

Question 4 :

A solid consisting of a right circular cone of height 12 cm and radius 6 cm standing on a hemisphere of radius 6 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of the water displaced out of the cylinder, if the radius of the cylinder is 6 cm and height is 18 cm.

Solution :

Volume of water displaced 

  =  Volume of water in the cylinder - (Volume of cone + Volume hemisphere)

  =   πr²h - [(1/3) πr²h +  (2/3)πr³]

  =   πr²h - (1/3) πr²h - (2/3)πr³

  =   πr² (h -(1/3)h - (2/3)r)

  =   (22/7)6² (18 -(1/3)(12) - (2/3)(6))

  =   (22/7) 36 (18 - 4 - 4)

  =   (22/7) 36 (10)

  =  1131.42 cm³

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.