A glass is in the shape of a frustum of a cone.

A glass is in the shape of a frustum of a cone.

The bottom of the glass is a curve of radius 2cm. A father pours water into the glass to a height of 9cm, while the
surface of the water is a circle of radius 6cm.
(a) Calculate the volume of the water in the glass.
(b) The son who is playing with marbles drops two spherical balls into the water. The water level in the glass rises by
1.5cm as a result.
Calculate:
(i) the volume of one marble.
(ii) the radius of a marble.

---

---

sharon kalunda answered the question on May 9, 2019 at 09:33

Exams With Marking Schemes

• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Grade 8
• Grade 9
• PP1
• PP2
• Playgroup
• Form 1
• Form 2
• Form 3
• Form 4

Related Questions

---

• The table below gives the marks scored by a group of students in an exam. (Solved)
  

  The table below gives the marks scored by a group of students in an exam.
  
  (a) Given that the mean mark was 32.125, find x.
  (b) State the modal class.
  (c) Calculate the interquartile range.

  Date posted: May 9, 2019 .    Answers (1)

• (a) Complete the table below for y = 8 - 10x - 3x². (Solved)
  

  (a) Complete the table below for y = 8 - 10x - 3x².
  
  (b) On the grid provided, draw the graph of y = 8 - 10x -3x²
  (c) State the equation of the line of symmetry of y = 8 - 10x - 3x²
  (d) Use your graph to solve:
  (i) 3x²+ 10x - 8 = 0
  (ii) 3x²+ 11x + 6 = 0

  Date posted: May 9, 2019 .    Answers (1)

• A ship sails from A to D through B and C. B is 500km on a bearing of N50°E from A. C is on a... (Solved)
  

  A ship sails from A to D through B and C. B is 500km on a bearing of N50°E from A. C is on a bearing of 340° from B and
  at a distance of 620km. The bearings of D from A and C are N20°W and 560°W respectively.
  (a) Using the scale 1cm to rep 100km, show the relative positions of A, B, C and D.
  (b) Find the distance of D from:
  (i) A
  (ii) C
  (c) Find the bearing of D from B.
  (d) If the ship was sailing at an average of 500km/h. Find how long the journey took. Give the
  answer to the nearest hour.

  Date posted: May 9, 2019 .    Answers (1)

• Evaluate the following expression (Solved)
  

  Evaluate the following expression
  

  Date posted: May 9, 2019 .    Answers (1)

• Given that 5x = 4y, evaluate (Solved)
  

  Given that 5x = 4y, evaluate
  

  Date posted: May 9, 2019 .    Answers (1)

• Find a 2 x 2 matrix m such that; (Solved)
  

  Find a 2 x 2 matrix m such that;
  

  Date posted: May 9, 2019 .    Answers (1)

• The angle of elevation of the top of a flag post from a point A on the level ground is 12°. The angle of elevation... (Solved)
  

  The angle of elevation of the top of a flag post from a point A on the level ground is 12°. The angle of elevation of the top
  of the flag post from another point B nearer to the flag post and 98m away from A is 34°. B is in between A and the
  bottom of the flag post and the three points are collinear. Find the height of the flag post to the nearest metre.

  Date posted: May 9, 2019 .    Answers (1)

• Pamba bought 4 mobile phones and 2 laptops for ksh, 108,000. Rebecca bought 3 mobile phones and 5 laptops from the same shop for ksh... (Solved)
  

  Pamba bought 4 mobile phones and 2 laptops for ksh, 108,000. Rebecca bought 3 mobile phones and 5 laptops from the same shop for ksh 228,000. How much will Juma pay for one mobile phone and 2 laptops.

  Date posted: May 9, 2019 .    Answers (1)

• The present ages of two children are 3 years and 5 years respectively. After how long will the sum of the squares of their ages be... (Solved)
  

  The present ages of two children are 3 years and 5 years respectively. After how long will the sum of the squares of
  their ages be 130?

  Date posted: May 9, 2019 .    Answers (1)

• Use logarithms to 4 d.p to evaluate: (Solved)
  

  Use logarithms to 4 d.p to evaluate:
  

  Date posted: May 9, 2019 .    Answers (1)

• Either by striding 48cm or 54cm, Joan takes an exact number of steps to cross the road. Find the least width of the road in metres. (Solved)
  

  Either by striding 48cm or 54cm, Joan takes an exact number of steps to cross the road. Find the least width of the road
  in metres.

  Date posted: May 9, 2019 .    Answers (1)

• The interior angles of an irregular polygon are 70° and 110° and the rest are each 144°. Determine the number of sides of the polygon. (Solved)
  

  The interior angles of an irregular polygon are 70° and 110° and the rest are each 144°. Determine the number of sides
  of the polygon.

  Date posted: May 9, 2019 .    Answers (1)

• Find a scalar K such that (Solved)
  

  Find a scalar K such that
  

  Date posted: May 9, 2019 .    Answers (1)

• A line L is perpendicular to 3y - 4x = 7. Determine the acute angle between L and the x-axis. (Solved)
  

  A line L is perpendicular to 3y - 4x = 7. Determine the acute angle between L and the x-axis.
  

  Date posted: May 9, 2019 .    Answers (1)

• Evaluate without using tables or a calculator. (Solved)
  

  Evaluate without using tables or a calculator.
  100^-1.5 X 32^0.2

  Date posted: May 9, 2019 .    Answers (1)

• a) Complete the table below for the values of sin 2x and 2 cos (x - 30^o) (Solved)
  

  a) Complete the table below for the values of sin 2x and 2 cos (x - 30^o)
  
  b) On the grid provided, use a suitable scale to draw the graphs of y = sin 2x and y = 2 cos (x - 30^o)
  for 0^o ≤ x ≤ 180^o
  c) Using the graph in part (b) above.
  i) Estimate the solution to the equation 2cos (x - 30^o) - sin 2x = 0 for 0^o ≤ x ≤ 180^o
  ii) Estimate the value of x for which 4 cos (x - 30^o) + 3 = 0

  Date posted: May 9, 2019 .    Answers (1)

• The table below shows marks scored by 40 candidates in an examination. (Solved)
  

  The table below shows marks scored by 40 candidates in an examination.
  
  a) Using an assumed mean of 45.5 estimate :
  i) Mean
  ii) Standard deviation
  b) Calculate the quartile deviation.

  Date posted: May 9, 2019 .    Answers (1)

• The sketch below shows curve y = 2x² + 4x + 3 and a straight line intersecting the curve at points A and B. (Solved)
  

  The sketch below shows curve y = 2x² + 4x + 3 and a straight line intersecting the curve at points A and B.
  
  If the x-intercepts is -3.5 and the y-intercept is 7, find :
  a) the equation of the straight line.
  b) the coordinates of A and B
  c) the area of the shaded region

  Date posted: May 9, 2019 .    Answers (1)

• In the figure below, ABCDEF is a wedge. BC = 6cm, DC = 8cm and ED = 15cm. (Solved)
  

  In the figure below, ABCDEF is a wedge. BC = 6cm, DC = 8cm and ED = 15cm.
  
  Find the :
  a) length BE
  b) angle between BE and the plane EDCF
  c) angle between plane ABDE and the plane EDCF
  d) volume of the wedge

  Date posted: May 9, 2019 .    Answers (1)

• Mrs Mureithi has 20 acres of land. She intends to grow maize and beans. She requires sh.2000 to plant an acre of maize and sh.4000 for... (Solved)
  

  Mrs Mureithi has 20 acres of land. She intends to grow maize and beans. She requires sh.2000 to plant an acre of maize
  and sh.4000 for an acre of beans. Twice the area to be planted with maize should not be less than one of beans. The
  total capital available is sh.60000. The estimated profit is sh.5000 for an acre of maize and sh.7000 for an acre of
  beans.
  By letting x and y to represent the area to be planted with maize and beans respectively.
  a) Find the inequalities to represent the information.
  b) On the grid provided, represent the inequalities and show the region which satisfy the condition.
  c) Determine the expected maximum profit.

  Date posted: May 9, 2019 .    Answers (1)