3D-Shapes Surface & volume

When balloons are inflated, they form spheres because they are trying to hold as much air as possible with as small a surface as possible. How much air, to the nearest cubic inch, is being held by a spherical balloon with a diameter of 10 inches?

• 167 cubed inches

• 1333 cubeb inches

• 524 cubed inches

• 4189 cubed inches

A cone is filled to its height of 3 inches with a liquid. The liquid is then poured into an empty cylinder with the same height and same radius as the cone. What is the height reached by the liquid in the cylinder?

• 3 in

• 2,5 in

• 2 in

• 1 in

Otto is sitting on 10 blocks of gold. The blocks are in the shape of right trapezoidal prisms. The trapezoidal base of the prism has bases of 10 inches and 7 inches with a height of 8 inches. The lateral edge of the prism is 19 inches. Upon how many total cubic inches of gold is he sitting?

• 8,930 cubic inches

• 12,920 cubic inches

• 15,300 cubic inches

• 25,840 cubic inches

At Theater A, popcorn is served in a box. At Theater B, popcorn is served in a cylindrical container. At home, Mom serves popcorn in a bowl (hemisphere in shape). Based upon the given dimensions, at which location are you getting the most popcorn?

• Theatre A

• Theatre B

• At home

The Great Pyramid of Egypt, built for Pharaoh Khufu around 2560 BC, is the oldest and largest of the three pyramids in Giza. Its square base measures 230.4 meters on a side and is 146.5 meters tall.The second tallest pyramid is the Pyramid of Khafre (son of Khufu) with a square base measuring 215.28Khafre's Pyramid meters on a side and 136.4 meters tall. What is the difference in volume between these two pyramids, to the nearest cubic meter?

• 210,717 cubic meters

• 485,102 cubic meters

• 259,228 cubic meters

• 744,330 cubic meters

A cone is filled to its height of 3 inches with a liquid. The liquid is then poured into an empty cylinder with the same height and same radius as the cone. What is the height reached by the liquid in the cylinder?

• 3 in

• 2,5 in

• 2 in

• 1 in

In the closed cylinder shown in the picture, the height is equal to the radius. The total surface area of the cylinder is 576 square inches. Find the exact length of the radius in inches.

• $\frac{4\sqrt{\pi}}{\pi}$

• $\frac{12\sqrt{\pi}}{\pi}$

• $\frac{16\sqrt{\pi}}{\pi}$

• $\frac{24\sqrt{\pi}}{\pi}$

The picture shows a right circular cylinder and a right circular cone with congruent bases and equal heights. If the cone section is removed from the cylinder, find the volume of the remaining section of the cylinder.

• $320\ \pi\ in^3$

• $640\ \pi\ in^3$

• $960\ \pi\ in^3$

• $1280\ \pi\ in^3$

A right square pyramid has a height of 15 cm. and a slant height of 25 cm.

What is the volume of the pyramid?

• 2400 squared cm

• 6000 squared cm

• 8000 squared cm

• 24000 squared cm

A sphere is placed in a cylinder such that the sphere touches (is tangent to) the top, bottom, and sides of the cylinder. The volume of the sphere is 972π cubic units. Find the volume of the cylinder.

• $216\ \pi\ units^3$

• $1458\ \pi\ units^3$

• $729\ \pi\ units^3$

• $1728\ \pi\ units^3$