Write the formula for the volume of a sphere.

Another day — let's solve it. 1. The volume of a spherical ball is 5,000 cm^3. What is the radius of the ball correct to one decimal place? (Use = 3.14) Step 1: Write the formula for the volume of a sphere. V = (4)/(3) r^3 Step 2: Substitute the given values into the formula. 5000 = (4)/(3) × 3.14 × r^3 Step 3: Isolate r^3. r^3 = (5000 × 3)/(4 × 3.14) r^3 = (15000)/(12.56) r^3 ≈ 1194.2675 Step 4: Calculate r by taking the cube root. r = [3]1194.2675 r ≈ 10.610 cm Step 5: Round the radius to one decimal place. r ≈ 10.6 cm The radius of the ball is 10.6 cm. 2. A cone has a diameter of 70 mm and a height of 100 mm. What is its volume to the nearest mm^3? (Use = 3.14) Step 1: Calculate the radius from the given diameter. r = diameter2 = 70 mm2 = 35 mm Step 2: Write the formula for the volume of a cone. V = (1)/(3) r^2 h Step 3: Substitute the given values into the formula. V = (1)/(3) × 3.14 × (35 mm)^2 × 100 mm V = (1)/(3) × 3.14 × 1225 mm^2 × 100 mm V = (1)/(3) × 384650 mm^3 V ≈ 128216.666... mm^3 Step 4: Round the volume to the nearest mm^3. V ≈ 128217 mm^3 The volume of the cone is 128217 mm^3. 3. Find the surface area of a box with dimensions 125 mm × 64 mm × 84 mm to the nearest mm^2. Step 1: Identify the dimensions of the box. Length l = 125 mm Width w = 64 mm Height h = 84 mm Step 2: Write the formula for the surface area of a rectangular box (cuboid). SA = 2(lw + lh + wh) Step 3: Substitute the dimensions into the formula. SA = 2((125 mm × 64 mm) + (125 mm × 84 mm) + (64 mm × 84 mm)) SA = 2(8000 mm^2 + 10500 mm^2 + 5376 mm^2) SA = 2(23876 mm^2) SA = 47752 mm^2 Step 4: The surface area is already an integer, so no rounding is needed to the nearest mm^2. The surface area of the box is 47752 mm^2. Send me the next one 📸