Math Problem Solver

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Exercise

1) Find the ratio between volume of cone and hemisphere when r and h are equal, i.e., 5 m.

2) Find the volume of hemisphere whose radius is:

(i) r = 0.7 cm

(ii) r = 5.6 m

(iii) r = 28 m

(iv) r = 7 m

(v) r = 3.5 cm

3) Find the volume of hemisphere whose diameter is:

(i) d = 14 cm

(ii) d = 7 cm

(iii) d = 35/2 cm

4) Find the volume of hemisphere whose CSA is 308 cm².

5) Find SA of hemisphere whose volume = 48π cm³.

6) Find the cost of plating inside of a hemisphere @ ₹5/cm². If its d = 14 cm.

7) The ratio of volume of cylinder and hemisphere is 3:2. Find the ratio between h and r if both have same radius.

8) If the radius of cone and cylinder are in ratio 3:2 and h = 2:3, find the ratio between their volumes.

9) The ratio of volumes of two spheres is 64:27, then find the ratio between their surface areas.

Test

Q1) If length, width, height, surface area and volume of cuboid are a, b, c, S, V respectively, show that

1/V = 2/S (a⁻¹ + b⁻¹ + c⁻¹).

Q2) Two cubes each volume 216 m³. Find the curved surface area of cube.

Q3) Three cubes of volume 1331 m³ each. Find cost of packaging @ ₹2/m².

Q4) Find the area leveled by roller of diameter 28 m and length 50 m.

Extra Questions (6.11.25)

1) Find the radius of cylinder whose h = 16 cm and volume = 32π cm³.

2) Find the height of cylinder whose diameter is 14 cm and its volume = 100π cm³.

3) What is the volume of cylinder whose h = 15 cm and area of base = 154 cm²?

4) Find the radius and height of cylinder whose V = 96π cm³. If the ratio of radius and height = 2:3.

5) Radius and height of cylinder is equal to r.

The ratio of CSA between cylinder and cone is 8:5.

Find the ratio of r and height if r and height of cylinder and cone are equal.

Extra Questions (7.11.25)

1) Circumference of circle is 10 cm and height is 4 cm. Find LSA of cylinder.

2) CSA of cylinder is 220 m² and diameter is 14 m. Find height.

3) Find volume of cylinder if total length (circumference) is 26 cm and h = 7 cm.

4) Find the area of water shower cylinder whose diameter = 7 cm and length = 30 cm.

5) Find the cost of leveling the ground by roller @ ₹5/m². If l = 8 m and dia = 3.5 m.

6) How much cardboard is required to make 10 models in the shape of cylinder of radius 10 cm and height 20 cm? @ ₹8/cm².

Additional Questions

Q2) Volume of cube is 343 cm³. If three cubes of same size placed vertically, find the area of packaging.

Q3) Two cubes each of volume 216 cm³ placed horizontally. Find the cost of packing @ ₹10/m².