SURFACE AREA AND VOLUME OF COMBINATION OF SOLIDS WORKSHEET

Problem 1 :

A play top is in the form of a hemisphere surmounted on a cone. The diameter of the hemisphere is 3.6 cm. The total height of the play top is 4.2 cm. Find its total surface area.

Solution

Problem 2 :

A solid is in the shape of a cylinder surmounted on a hemisphere. If the diameter and the total height of the solid are 21 cm,25.5 cm respectively, then find its volume.

Solution

Problem 3 :

A capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. If the length of the entire capsule is 14 mm and diameter of the capsule is 5 mm, find its surface area.

Solution

Problem 4 :

A tent is in the shape of right circular cylinder surmounted by a cone. The total height and diameter of the base are 13.5 m and 28 m. If the height of the cylindrical portion is 3 m, find the total surface area of the tent.

Solution

Problem 5 :

Using clay, a student made a right circular cone of height 48 cm and base radius 12 cm. Another student reshapes it in the form of a sphere. Find the radius of the sphere.

Solution

Problem 6 :

The radius of a solid sphere us 24 cm. It is melted and drawn into a long wire of uniform cross section. Find the length of the wire if its radius is 1.2 mm.

Solution

Problem 7 :

A right circular conical vessel whose internal radius is 5 cm and height is 24 cm is full of water. The water is emptied into an empty cylindrical vessel with internal radius 10 cm. Find the height of the water level in the cylindrical vessel.

Solution

Problem 8 :

A solid sphere of diameter 6 cm is dropped into a right circular cylindrical vessel with diameter 12 cm, which is partly filled with water, If the sphere is completely submerged in water, how much does the water level in the cylindrical vessel.

Solution

Problem 9 :

Though a cylindrical pipe of internal radius 7 cm, water flows out at the rate of 5 cm/sec. Calculate the volume of water (in liters) discharged through the pipe in half an hour.

Solution

Problem 10 :

Water in a cylindrical tank of diameter 4 m and height 10 m is released through a cylindrical pipe of diameter 10 cm at the rate of 2.5 km/hr. How much time will it take to empty the half of  the tank? Assume that the tank is full of water to begin with.

Solution

Problem 1 :

If the curved surface area of solid sphere is 98.56 cm², then find the radius of the sphere.

Solution

Problem 2 :

If the curved surface area of the solid hemisphere is 2772 sq.cm, then find its total surface area.

Solution

Problem 3 :

Radii of two solid hemispheres are in the ratio 3:5. Find the ratio of their curved surface areas and the ratio of their total surface areas.

Solution

Problem 4 :

A hemispherical bowl has a radius of 15 cm. If it is filled completely with water and covered with a lid,

(a) find the volume of the water

(b) find the surface area of the bowl (including the lid). Give your answers to 3 significant figures.

Take π = 3.142

Solution

Problem 5 :

A Puffer fish is able to “puff up” when threatened by gulping water and inflating its body. The puffer fish is approximately a sphere with a diameter of 5 inches. Its surface area when inflated is about 1.5 times its normal surface area.

What is the surface area of the fish when it is not puffed up?

Solution

Problem 6 :

A sphere has radius 4.5 cm. Find the volume and surface area of the sphere. Give your answers to 3 significant figures.

Take π = 3.142

Solution

Problem 7 :

Basketballs used in professional games must have a circumference of 29 1/2 inches. What is the surface area of a basketball used in a professional game?

Solution

Problem 8 :

A bowl has the form of a hollow hemisphere of radius 8.4 cm. Find the external surface area and the volume of the bowl. Give your answers to 0 significant figures. Take π = 3.142

Solution

Problem 9 :

Find the radius of an opened hemisphere whose surface area is 1762 cm² Give your answers to 3 significant figures. Take π = 3.142

Solution

Problem 10 :

A sphere has radius 12.6 cm. Find the volume and surface area. Give your answers to 3 significant figures. Take π = 3.142

Solution

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