A solid metal sphere of radius 7 cm is melted and recast into smaller spheres of radius 1.4 cm. a) Find the number of smaller spheres obtained. b) If the metal used costs Ksh 450 per cubic centimetre, find the total cost of the metal in the original sphere. (Take pi = 22/7)

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Asked on July 3, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-07-03T10:05:09.692Z

here are the solutions to the questions from the image, explained in English: 4. a) Find the number of smaller spheres obtained. Step 1: Calculate the volume of the large sphere. The radius of the large sphere, R = 7 cm. The volume of a sphere is given by the formula V = (4)/(3) R^3. V_L = (4)/(3) (7)^3 Step 2: Calculate the volume of one small sphere. The radius of a small sphere, r = 1.4 cm. V_S = (4)/(3) (1.4)^3 Step 3: Find the number of smaller spheres. The number of smaller spheres (N) is the total volume of the large sphere divided by the volume of one small sphere. N = (V_L)/(V_S) = (4)/(3) (7)^3(4)/(3) (1.4)^3 Cancel out (4)/(3): N = ((7)^3)/((1.4)^3) = ((7)/(1.4))^3 N = (5)^3 = 125 The number of smaller spheres obtained is 125. b) If the metal used costs Ksh 450 per cubic centimetre, find the total cost of the metal in the original sphere. Step 1: Calculate the volume of the original sphere using = (22)/(7). The radius of the original sphere, R = 7 cm. V_L = (4)/(3) R^3 = (4)/(3) × (22)/(7) × (7)^3 V_L = (4)/(3) × (22)/(7) × 343 V_L = (4 × 22 × 49)/(3) = (4312)/(3) cm^3 Step 2: Calculate the total cost. The cost per cubic centimetre is Ksh 450. Total cost = Volume of original sphere × Cost per cubic centimetre. Total Cost = (4312)/(3) × 450 Total Cost = 4312 × 150 = 646800 The total cost of the metal in the original sphere is Ksh 646,800. 5. a) Form an equation in x and solve it. Step 1: Formulate the equation. The exterior angle of a regular polygon is x^. The interior angle of the regular polygon is 5x^. The sum of an interior angle and its corresponding exterior angle is always 180^. x + 5x = 180 Step 2: Solve the equation for x. Combine like terms: 6x = 180 Divide by 6: x = (180)/(6) x = 30 The equation is x + 5x = 180 and the value of x is 30. What's next?

Accepted Answer · 2026-07-03T10:05:09.692Z

here are the solutions to the questions from the image, explained in English: 4. a) Find the number of smaller spheres obtained. Step 1: Calculate the volume of the large sphere. The radius of the large sphere, R = 7 cm. The volume of a sphere is given by the formula V = (4)/(3) R^3. V_L = (4)/(3) (7)^3 Step 2: Calculate the volume of one small sphere. The radius of a small sphere, r = 1.4 cm. V_S = (4)/(3) (1.4)^3 Step 3: Find the number of smaller spheres. The number of smaller spheres (N) is the total volume of the large sphere divided by the volume of one small sphere. N = (V_L)/(V_S) = (4)/(3) (7)^3(4)/(3) (1.4)^3 Cancel out (4)/(3): N = ((7)^3)/((1.4)^3) = ((7)/(1.4))^3 N = (5)^3 = 125 The number of smaller spheres obtained is 125. b) If the metal used costs Ksh 450 per cubic centimetre, find the total cost of the metal in the original sphere. Step 1: Calculate the volume of the original sphere using = (22)/(7). The radius of the original sphere, R = 7 cm. V_L = (4)/(3) R^3 = (4)/(3) × (22)/(7) × (7)^3 V_L = (4)/(3) × (22)/(7) × 343 V_L = (4 × 22 × 49)/(3) = (4312)/(3) cm^3 Step 2: Calculate the total cost. The cost per cubic centimetre is Ksh 450. Total cost = Volume of original sphere × Cost per cubic centimetre. Total Cost = (4312)/(3) × 450 Total Cost = 4312 × 150 = 646800 The total cost of the metal in the original sphere is Ksh 646,800. 5. a) Form an equation in x and solve it. Step 1: Formulate the equation. The exterior angle of a regular polygon is x^. The interior angle of the regular polygon is 5x^. The sum of an interior angle and its corresponding exterior angle is always 180^. x + 5x = 180 Step 2: Solve the equation for x. Combine like terms: 6x = 180 Divide by 6: x = (180)/(6) x = 30 The equation is x + 5x = 180 and the value of x is 30. What's next?

A solid metal sphere of radius 7 cm is melted and recast into smaller spheres of radius 1.4 cm. a) Find the number of smaller spheres obtained. b) If the metal used costs Ksh 450 per cubic centimetre, find the total cost of the metal in the original sphere. (Take pi = 22/7)

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A solid metal sphere of radius 7 cm is melted and recast into smaller spheres of radius 1.4 cm. a) Find the number of smaller spheres obtained. b) If the metal used costs Ksh 450 per cubic centimetre, find the total cost of the metal in the original sphere. (Take pi = 22/7)

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