Volume
Surface Area
Circles
100
A rectangular prism of volume 3200 mm3 has a rectangular base of length 10 mm and width 8 mm. Find the height h of the prism.
- Volume is given by by
volume = length * width * height = 10 mm * 8 mm * h = 3200 mm3 - Solve for h
h = 3200 mm3 / 80 mm2 = 40 mm
[ ANSWER IS 40 ]
100
Find the total surface area of a closed cylindrical container with radius 5 cm and a height of 34 cm.
The total surface area A of a cylinder is given by the sum of the area of the lateral surface plus the areas of the base and bottom of the container.
A = 2 × radius × π × height + π × radius2 + π × radius2
= 2 × 5 × π × 34 + π × 52 + π × 52
= 340 π + 25 π + 25 π = 390 π square centimeters
= 1224.6 square centimeters (using π = 3.14)
[ ANSWER IS 1224.6 ]
100
Find the area of a circle with a diameter of 10 inches.
78.55
200
The triangular base of a prism is a right triangle of sides a and b = 2a. The height h of the prism is equal to 10 mm and its volume is equal to 40 mm3, find the lengths of the sides a and b of the triangle.
4mm
200
Find the total surface area of the box open at the top.
Area of the open box is equal to
The areas of the front and back faces + the areas of the left and right faces + the area ot bottom
= 2(12 × 11) + 2(9 × 11) + 9 × 12 = 570 square cm
[ 570 SQUARE CM IS ANSWER ]
200
Find the area of a circle with a radius of 10 inches.
314.2 square inches
300
Find the volume of the given L-shaped rectangular structure.
24000mm3
300
Find the surface area of the triangular prism shown below. The height is 8, the length is 14, the width is 12, and the slant height is 10.
544 units2
400
Find x so that the volume of the U-shaped rectangular structure is equal to 165 cm3.
x= 5
400
Find the surface area of the cereal box. The height is 10cm, the width 20cm and the length is 5cm.
The surface area of the cereal box is 1700cm2
500
Find the volume of the hexagonal prism whose base is a regular hexagon of side x = 10 cm.
6235.4cm3
500
Find the surface area of the square pyramid shown below. The height is 6 and the length and width is 8.
160 units2