Volume and Surface Area of Composite Solids Worksheet

VOLUME AND SURFACE AREA OF COMPOSITE SOLIDS WORKSHEET

(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

(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

(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

(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

(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

(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

(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

(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

(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

(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

Answer Key

1) Total surface area of the play top = 11.88 Π cm²

2) Volume of solid shape = 7623 cm³.

3) Total surface area of capsule = 220 mm².

4) total surface area of the tent is 1034 cm³

5) Radius of sphere is 12 cm.

6) the required height height is 12.8 km.

7) height of water is 2 cm.

8) Therefore increased water level is 1 cm.

9) the quantity of water discharged is 1386 liters.

10) time taken to empty the half of the tank is 3 hour and 12 minute.

Answer Key

1) The surface area before the hole was drilled was 3,720 sq.cm.

2) The surface area of the part of the plant stand she will stain is 976 sq.in.

1) Allie has two aquariums connected by a small square prism. Find the volume of the double aquarium.

Solution

2) The figure is composed of a rectangular prism and a triangular prism. Find the volume of the figure.

Solution

3) The figure is composed of a rectangular prism and a triangular prism. Find the volume of the figure.

Solution

Answer Key

1) The volume of the aquarium is 74 cubic ft.

2) The volume of the given figure is 6825 cubic in.

3) The volume of the given figure is 360 cubic ft.

1. Erin is making a jewelry box of wood in the shape of a rectangular prism. The jewelry box will have the dimensions shown below. The cost of painting the exterior of the box is $0.50 per square in. How much does Erin have to spend to paint the jewelry box ?

Solution

2. A metal box that is in the shape of rectangular prism has the following dimensions. The length is 9 inches, width is 2 inches, and height is 1 1/2 inches. Find the total cost of silver coating for the entire box.

Solution

3. Cherise is setting up her tent. Her tent is in the shape of a trapezoidal prism shown below. How many cubic feet of space are in her tent ?