Bissoy.com
Doctors Medicines MCQs Q&A

A pyramid having square base of side 16 cm is cut horizontally at some height. The frustum thus formed has the volume equal to 834 cm3. If the side of square base of upper surface of the frustum is 7 cm, the height at which the cut was made is 6 cm from the base, then find the total height of the original pyramid.

A pyramid having square base of side 16 cm is cut horizontally at some height. The frustum thus formed has the volume equal to 834 cm3. If the side of square base of upper surface of the frustum is 7 cm, the height at which the cut was made is 6 cm from the base, then find the total height of the original pyramid. Correct Answer 32/3 cm

When pyramid is cut at height 6 cm, one part will be frustum of height 6 cm and other part is a pyramid only.

The smaller pyramid will have the square base of side 7 cm (As the side of square base of upper surface of the frustum is 7 cm)

Suppose the height of smaller pyramid = h cm

∴ Total height of the original pyramid = (6 + h) cm

∴ Volume of original pyramid = Volume of smaller pyramid + Volume of frustum

⇒ 1/3 × (16)2 × (6 + h) = 1/3 × (7)2 × h + 1/3 × 6 ×

⇒ 256/3 × (6 + h) = 49/3 × h + 2 ×

⇒ 1536 + 256h = 49h + 2502

⇒ 207h = 966

⇒ h = 14/3 cm

∴ Total height of the original pyramid = 6 + 14/3 = 32/3 cm

Related Questions

A square pyramid shaped toy is cut horizontally from 9 cm height to make a frustum. The base side and upper side of the frustum are 20 cm and 12 cm respectively. What is the volume of the square pyramid frustum?
A pyramid shaped toy with square base of side 12 cm and Lateral height 16 cm is cut horizontally at Lateral height 4 cm from the base to form a frustum, then what will be the total surface area of the frustum?
The base of a right pyramid is a square of side 10 cm. 4 rods with maximum possible length have been kept in the pyramid. The volume of the pyramid (without keeping the rods inside) is 400 cm3. The radius of the base of all the rods is 0.7 cm. What will be the approximate volume of the remaining part of the pyramid (when rods are kept inside the pyramid)?
Given below are three quantities named 1, 2 and 3. Based on the given information, you have to determine the relationship between the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. Quantity 1: Area of the innermost square. A square is made by joining the midpoints of a square of area 200 sq. m. The outermost square is called Square 1, The square inside it is called Square 2. The next square is made by joining midpoints of square 2 and is called Square 3. This process goes on. Square 5 is the innermost square. Quantity 2: A man starts with a speed of 10 km/hr. He increases his speed by 10 km/hr every hour at the start and drives at the same speed for that hour. If he traveled a total distance of 550 km. Find the time Quantity 3: Height of cylinder Its volume is equal to the volume of a cone whose radius is 14 cm and height is 39.3 cm. The radius of the cylinder is 14 cm
A pyramid has a square base. The side of square is 12 cm and height of pyramid is 21 cm. The pyramid is cut into 3 parts by 2 cuts parallel to its base. The cuts are at height of 7 cm and 14 cm respectively from the base. What is the difference (in cm3) in the volume of top most and bottom most part?
A right circular cone of base radius 15 cm and height 40 cm is cut parallel to its base so as to obtain a frustum of height 10 cm and volume of 2000π cm3. What is the radius of the upper base of the frustum?
If the height of the square base pyramid is equal to the side of the Tetrahedron whose height is 4√6 cm and the side of the square base pyramid is 7 cm. What will be the volume of the square base pyramid?
“What is the different between height and radius of solid cylinder?” Which of the following option is sufficient alone to find the answer? A) A solid cylinder is made by melting a solid sphere. The radius of cylinder is 3 times the radius of a circle whose area is 154 sq.m. Height of cylinder is equal to the height of cone whose volume is 2772 cubic meters. B) Area of a rectangle whose longer side is ¾ times the radius of a solid cylinder, is 168 sq.m and, Volume of solid cylinder is 2772 cubic meters and its height is 18 m. C) A metallic cone of radius 15m and height 35m is melted into the solid cylinder of radius equal to the radius of a circle whose area is equal to the area of rectangle whose sides are in the ratio 4 : 3 respectively. D) The curved surface area of the solid cylinder is 3 time the surface area of a sphere of radius 7m and height of cylinder is equal to the height of a metallic cone whose curved surface area is 308 sq.m. 
A cone of height of 32 cm is cut at a height of ‘h’ cm from the base by a plane parallel to the base to form a frustum. If volumes of the complete cone and frustum are 3584 cm3 and 2709 cm3, then what will be the value of ‘h’?
A cone of radius 7 cm and slant height 15 cm was cut horizontally, resulting in a smaller cone and a frustum of a cone. If the ratio of the curved surface area of the upper and the lower part is 1 : 2, What will be the slant height of the frustum formed?